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INSTRUCTOR’S MANUAL TO ACCOMPANY
ALPHA (incomplete) VERSION DATED: August 28, 2001
Database System Concepts
Fourth Edition
Abraham Silberschatz
Bell Laboratories
Henry F. Korth
Bell Laboratories
S. Sudarshan
Indian Institute of Technology, Bombay
c
Copyright 2001
A. Silberschatz, H. Korth, and S. Sudarshan
Contents
Preface 1
Chapter 1
Introduction
Exercises 4
Chapter 2
Entity Relationship Model
Exercises 9
Chapter 3
Relational Model
Exercises 30
Chapter 4
SQL
Exercises 42
Chapter 5
Other Relational Languages
Exercises 58
Chapter 6
Integrity and Security
Exercises 74
iii
iv
Contents
Chapter 7
Relational-Database Design
Exercises 84
Chapter 8
Object-Oriented Databases
Exercises 98
Chapter 9
Object-Relational Databases
Exercises 109
Chapter 10 XML
Exercises 119
Chapter 11
Storage and File Structure
Exercises 129
Chapter 12 Indexing and Hashing
Exercises 141
Chapter 13 Query Processing
Exercises 155
Chapter 14 Query Optimization
Exercises 166
Chapter 15 Transactions
Exercises 175
Chapter 16 Concurrency Control
Exercises 182
Chapter 17 Recovery System
Exercises 194
Contents
Chapter 18 Database System Architectures
Exercises 201
Chapter 19 Distributed Databases
Exercises 208
Chapter 20 Parallel Databases
Exercises 217
Chapter 21 Application Development and Administration
Exercises 225
Chapter 22 Advanced Querying and Information Retrieval
Exercises 232
Chapter 23 Advanced Data Types and New Applications
Exercises 241
Chapter 24 Advanced Transaction Processing
Exercises 249
v
Preface
This volume is an instructor’s manual for the 4th edition of Database System Concepts
by Abraham Silberschatz, Henry F. Korth and S. Sudarshan. It contains answers to
the exercises at the end of each chapter of the book. Before providing answers to the
exercises for each chapter, we include a few remarks about the chapter. The nature of
these remarks vary. They include explanations of the inclusion or omission of certain
material, and remarks on how we teach the chapter in our own courses. The remarks
also include suggestions on material to skip if time is at a premium, and tips on
software and supplementary material that can be used for programming exercises.
Beginning with this edition, solutions for some problems have been made available on the Web. These problems have been marked with a “ * ” in the instructor’s
manual.
The Web home page of the book, at http://www.bell-labs.com/topic/books/db-book,
contains a variety of useful information, including up-to-date errata, online appendices describing the network data model, the hierarchical data model, and advanced
relational database design, and model course syllabi. We will periodically update the
page with supplementary material that may be of use to teachers and students.
We provide a mailing list through which users can communicate among themselves and with us. If you wish to be on the list, please send an email to
db-book@research.bell-labs.com
including your name, affiliation, title, and electronic mail address.
We would appreciate it if you would notify us of any errors or omissions in the
book, as well as in the instructor’s manual. Although we have tried to produce an
instructor’s manual which will aid all of the users of our book as much as possible,
there can always be improvements. These could include improved answers, additional questions, sample test questions, programming projects, suggestions on alternative orders of presentation of the material, additional references, and so on.
If you would like to suggest any such improvements to the book or the instructor’s manual, we would be glad to hear from you. Internet electronic mail should
1
2
Preface
be addressed to db-book@research.bell-labs.com. Physical mail may be sent to Avi
Silberschatz, Bell Laboratories, Room 2T-310, 600 Mountain Avenue, Murray Hill, NJ
07974, USA. All contributions that we make use of will, of course, be properly credited to their contributor.
Nilesh Dalvi, Sumit Sanghai, Gaurav Bhalotia and Arvind Hulgeri did the bulk
of the work in preparing the instructors manual for the 4th edition. This manual is
derived from the manuals for the earlier editions. The manual for the 3rd edition was
prepared by K. V. Raghavan with help from Prateek R. Kapadia, Sara Strandtman
helped with the instructor manual for the 2nd and 3rd editions, while Greg Speegle
and Dawn Bezviner helped us to prepare the instructor’s manual for the 1st edition.
A. S.
H. F. K.
S. S.
Instructor Manual Version 4.0.0
C H A P T E R
1
Introduction
Chapter 1 provides a general overview of the nature and purpose of database systems. The most important concept in this chapter is that database systems allow data
to be treated at a high level of abstraction. Thus, database systems differ significantly
from the file systems and general purpose programming environments with which
students are already familiar. Another important aspect of the chapter is to provide
motivation for the use of database systems as opposed to application programs built
on top of file systems. Thus, the chapter motivates what the student will be studying
in the rest of the course.
The idea of abstraction in database systems deserves emphasis throughout, not
just in discussion of Section 1.3. The overview of the structure of databases, starting
from Section 1.4 is, of necessity, rather brief, and is meant only to give the student
a rough idea of some of the concepts. The student may not initially be able to fully
appreciate the concepts described here, but should be able to do so by the end of the
course.
The specifics of the E-R, relational, and object-oriented models are covered in later
chapters. These models can be used in Chapter 1 to reinforce the concept of abstraction, with syntactic details deferred to later in the course.
If students have already had a course in operating systems, it is worthwhile to
point out how the OS and DBMS are related. It is useful also to differentiate between
concurrency as it is taught in operating systems courses (with an orientation towards
files, processes, and physical resources) and database concurrency control (with an
orientation towards granularity finer than the file level, recoverable transactions, and
resources accessed associatively rather than physically). If students are familiar with
a particular operating system, that OS’s approach to concurrent file access may be
used for illustration.
3
4
Chapter 1
Introduction
Exercises
1.1 List four significant differences between a file-processing system and a DBMS.
Answer: Some main differences between a database management system and
a file-processing system are:
• Both systems contain a collection of data and a set of programs which access
that data. A database management system coordinates both the physical
and the logical access to the data, whereas a file-processing system coordinates only the physical access.
• A database management system reduces the amount of data duplication by
ensuring that a physical piece of data is available to all programs authorized
to have access to it, whereas data written by one program in a file-processing
system may not be readable by another program.
• A database management system is designed to allow flexible access to data
(i.e., queries), whereas a file-processing system is designed to allow predetermined access to data (i.e., compiled programs).
• A database management system is designed to coordinate multiple users
accessing the same data at the same time. A file-processing system is usually
designed to allow one or more programs to access different data files at
the same time. In a file-processing system, a file can be accessed by two
programs concurrently only if both programs have read-only access to the
file.
1.2 This chapter has described several major advantages of a database system. What
are two disadvantages?
Answer: Two disadvantages associated with database systems are listed below.
a. Setup of the database system requires more knowledge, money, skills, and
time.
b. The complexity of the database may result in poor performance.
1.3 Explain the difference between physical and logical data independence.
Answer:
• Physical data independence is the ability to modify the physical scheme
without making it necessary to rewrite application programs. Such modifications include changing from unblocked to blocked record storage, or from
sequential to random access files.
• Logical data independence is the ability to modify the conceptual scheme
without making it necessary to rewrite application programs. Such a modification might be adding a field to a record; an application program’s view
hides this change from the program.
1.4 List five responsibilities of a database management system. For each responsibility, explain the problems that would arise if the responsibility were not discharged.
Answer: A general purpose database manager (DBM) has five responsibilities:
a. interaction with the file manager.
Exercises
b.
c.
d.
e.
5
integrity enforcement.
security enforcement.
backup and recovery.
concurrency control.
If these responsibilities were not met by a given DBM (and the text points
out that sometimes a responsibility is omitted by design, such as concurrency
control on a single-user DBM for a micro computer) the following problems can
occur, respectively:
a. No DBM can do without this, if there is no file manager interaction then
nothing stored in the files can be retrieved.
b. Consistency constraints may not be satisfied, account balances could go below the minimum allowed, employees could earn too much overtime (e.g.,
hours > 80) or, airline pilots may fly more hours than allowed by law.
c. Unauthorized users may access the database, or users authorized to access
part of the database may be able to access parts of the database for which
they lack authority. For example, a high school student could get access
to national defense secret codes, or employees could find out what their
supervisors earn.
d. Data could be lost permanently, rather than at least being available in a consistent state that existed prior to a failure.
e. Consistency constraints may be violated despite proper integrity enforcement in each transaction. For example, incorrect bank balances might be
reflected due to simultaneous withdrawals and deposits, and so on.
1.5 What are five main functions of a database administrator?
Answer: Five main functions of a database administrator are:
•
•
•
•
•
To create the scheme definition
To define the storage structure and access methods
To modify the scheme and/or physical organization when necessary
To grant authorization for data access
To specify integrity constraints
1.6 List seven programming languages that are procedural and two that are nonprocedural. Which group is easier to learn and use? Explain your answer.
Answer: Programming language classification:
• Procedural: C, C++, Java, Basic, Fortran, Cobol, Pascal
• Non-procedural: Lisp and Prolog
Note: Lisp and Prolog support some procedural constructs, but the core of both
these languages is non-procedural.
In theory, non-procedural languages are easier to learn, because they let the
programmer concentrate on what needs to be done, rather than how to do it. This
is not always true in practice, especially if procedural languages are learned
first.
6
Chapter 1
Introduction
1.7 List six major steps that you would take in setting up a database for a particular
enterprise.
Answer: Six major steps in setting up a database for a particular enterprise are:
• Define the high level requirements of the enterprise (this step generates a
document known as the system requirements specification.)
• Define a model containing all appropriate types of data and data relationships.
• Define the integrity constraints on the data.
• Define the physical level.
• For each known problem to be solved on a regular basis (e.g., tasks to be
carried out by clerks or Web users) define a user interface to carry out the
task, and write the necessary application programs to implement the user
interface.
• Create/initialize the database.
1.8 Consider a two-dimensional integer array of size n × m that is to be used in
your favorite programming language. Using the array as an example, illustrate
the difference (a) between the three levels of data abstraction, and (b) between
a schema and instances.
Answer: Let tgrid be a two-dimensional integer array of size n × m.
a.
b.
• The physical level would simply be m × n (probably consecutive) storage locations of whatever size is specified by the implementation (e.g.,
32 bits each).
• The conceptual level is a grid of boxes, each possibly containing an integer, which is n boxes high by m boxes wide.
• There are 2m×n possible views. For example, a view might be the entire
array, or particular row of the array, or all n rows but only columns 1
through i.
• Consider the following Pascal declarations:
type tgrid = array[1..n, 1..m] of integer;
var vgrid1, vgrid2 : tgrid
Then tgrid is a schema, whereas the value of variables vgrid1 and vgrid2
are instances.
• To illustrate further, consider the schema array[1..2, 1..2] of integer. Two
instances of this scheme are:
1
7
16
89
17 90
412 8
C H A P T E R
2
Entity Relationship Model
This chapter introduces the entity-relationship model in detail. The chapter covers
numerous features of the model, several of which can be omitted depending on the
planned coverage of the course. Weak entity sets (Section 2.6), design constraints
(Section 2.7.4) and aggregation (Section 2.7.5), and the corresponding subsections of
Section 2.9 (Reduction of an E-R Schema to Tables) can be omitted if time is short. We
recommend covering specialization (Section 2.7.1) at least in some detail, since it is
an important concept for object-oriented databases (Chapter 8).
The E-R model itself and E-R diagrams are used often in the text. It is important
that students become comfortable with them. The E-R model is an excellent context
for the introduction of students to the complexity of database design. For a given
enterprise there are often a wide variety of E-R designs. Although some choices are
arbitrary, it is often the case that one design is inherently superior to another. Several
of the exercises illustrate this point. The evaluation of the goodness of an E-R design
requires an understanding of the enterprise being modeled and the applications to
be run. It is often possible to lead students into a debate of the relative merits of
competing designs and thus illustrate by example that understanding the application
is often the hardest part of database design.
Considerable emphasis is placed on the construction of tables from E-R diagrams.
This serves to build intuition for the discussion of the relational model in the subsequent chapters. It also serves to ground abstract concepts of entities and relationships
into the more concrete concepts of relations. Several other texts places this material
along with the relational data model, rather than in the E-R model chapter. Our motivation for placing this material here is help students to appreciate how E-R data
models get used in reality, while studying the E-R model rather than later on.
The material on conversion of E-R diagrams to tables in the book is rather brief
in some places, the book slides provide better coverage of details that have been left
implicit in the book.
7
8
Chapter 2
Entity Relationship Model
Changes from 3rd edition:
In the fourth edition we have updated several examples, including ternary relations (employee, branch, job instead of customer, loan, branch) and aggregation (manages
instead of loan-officer), to make them more realistic. We have also added more examples, for instance for specialization we use person, customer and employee as the
main example, instead of account, checking-account and savings-account, which also
makes the example more realistic. We have replaced the US centric social-security by
the more global (and more realistic) customer-id and employee-id.
We have added notation to make disjointedness constraints and total participation
explicit (overlapping and partial participation are the default). We have introduced
alternative E-R notations since many real world applications use alternative notations. We have also provided a brief introduction to UML class diagrams, which are
being used increasingly in place of E-R diagrams, in tools such as Oracle designer.
We have dropped coverage of existence dependencies since total participation constraints provide a very similar constraint. The distinction between total participation
and existence dependencies is too minor to be of practical use, and only confuses
students.
Design issues are discussed in more detail.
Exercises
model
address
driver-id
9
license
name
person
owns
driver
year
location
car
report-number
participated
date
accident
damage-amount
Figure 2.1
E-R diagram for a Car-insurance company.
Exercises
2.1 Explain the distinctions among the terms primary key, candidate key, and superkey.
Answer: A superkey is a set of one or more attributes that, taken collectively, allows us to identify uniquely an entity in the entity set. A superkey may contain
extraneous attributes. If K is a superkey, then so is any superset of K. A superkey
for which no proper subset is also a superkey is called a candidate key. It is possible that several distinct sets of attributes could serve as candidate keys. The
primary key is one of the candidate keys that is chosen by the database designer
as the principal means of identifying entities within an entity set.
2.2 Construct an E-R diagram for a car-insurance company whose customers own
one or more cars each. Each car has associated with it zero to any number of
recorded accidents.
Answer: See Figure 2.1
2.3 Construct an E-R diagram for a hospital with a set of patients and a set of medical doctors. Associate with each patient a log of the various tests and examinations conducted.
Answer: See Figure 2.2
2.4 A university registrar’s office maintains data about the following entities: (a)
courses, including number, title, credits, syllabus, and prerequisites; (b) course
offerings, including course number, year, semester, section number, instructor(s),
timings, and classroom; (c) students, including student-id, name, and program;
and (d) instructors, including identification number, name, department, and title. Further, the enrollment of students in courses and grades awarded to students in each course they are enrolled for must be appropriately modeled.
Construct an E-R diagram for the registrar’s office. Document all assumptions
that you make about the mapping constraints.
Answer: See Figure 2.3.
In the answer given here, the main entity sets are student, course, course-offering,
10
Chapter 2
Entity Relationship Model
insurance
date−admitted
name
date−checked−out
ss#
patients
test−log
test_id
Dr−Patient
test
test_name
date
time
Figure 2.2
sid
student
name
dss#
result
name
specialization
E-R diagram for a hospital.
secno
time
room
course−
offerings
enrols
year
program
doctors
performed_by
iid
instructor
teaches
semester
name
dept
title
grade
is
offered
syllabus
courseno
prerequisite
requires
course
title
maincourse
credits
Figure 2.3
E-R diagram for a university.
and instructor. The entity set course-offering is a weak entity set dependent on
course. The assumptions made are :
a. a class meets only at one particular place and time. This E-R diagram cannot
model a class meeting at different places at different times.
b. There is no guarantee that the database does not have two classes meeting
at the same place and time.
2.5 Consider a database used to record the marks that students get in different exams of different course offerings.
Exercises
sid
name
secno
time
student
year
marks
program
eid
exam
name
Figure 2.4
room
course−
offerings
takes
11
courseno
semester
time
place
E-R diagram for marks database.
a. Construct an E-R diagram that models exams as entities, and uses a ternary
relationship, for the above database.
b. Construct an alternative E-R diagram that uses only a binary relationship
between students and course-offerings. Make sure that only one relationship
exists between a particular student and course-offering pair, yet you can
represent the marks that a student gets in different exams of a course offering.
Answer:
a. See Figure 2.4
b. See Figure 2.5
2.6 Construct appropriate tables for each of the E-R diagrams in Exercises 2.2 to
2.4.
Answer:
a. Car insurance tables:
person (driver-id, name, address)
car (license, year, model)
accident (report-number, date, location)
participated(driver-id, license, report-number, damage-amount)
b. Hospital tables:
patients (patient-id, name, insurance, date-admitted, date-checked-out)
doctors (doctor-id, name, specialization)
test (testid, testname, date, time, result)
doctor-patient (patient-id, doctor-id)
test-log (testid, patient-id) performed-by (testid, doctor-id)
12
Chapter 2
Entity Relationship Model
sid
name
student
secno
time
course−
offerings
takes
year
program
marks
courseno
semester
examof
exam
name
Figure 2.5
room
time
place
Another E-R diagram for marks database.
c. University registrar’s tables:
student (student-id, name, program)
course (courseno, title, syllabus, credits)
course-offering (courseno, secno, year, semester, time, room)
instructor (instructor-id, name, dept, title)
enrols (student-id, courseno, secno, semester, year, grade)
teaches (courseno, secno, semester, year, instructor-id)
requires (maincourse, prerequisite)
2.7 Design an E-R diagram for keeping track of the exploits of your favourite sports
team. You should store the matches played, the scores in each match, the players
in each match and individual player statistics for each match. Summary statistics should be modeled as derived attributes.
Answer: See Figure 2.6
2.8 Extend the E-R diagram of the previous question to track the same information
for all teams in a league.
Answer: See Figure 2.7 Note that a player can stay in only one team during a
season.
2.9 Explain the difference between a weak and a strong entity set.
Answer: A strong entity set has a primary key. All tuples in the set are distinguishable by that key. A weak entity set has no primary key unless attributes of
the strong entity set on which it depends are included. Tuples in a weak entity
set are partitioned according to their relationship with tuples in a strong entity
Exercises
matchid
date
stadium
own _score
opp_score
Figure 2.6
season_score
E-R diagram for favourite team statistics.
score
age
name
played
match
date
player
score
stadium
matchid
age
name
played
match
opponent
13
player
season_score
score
team_played
player_of
result
team
name
Figure 2.7
ranking
E-R diagram for all teams statistics.
set. Tuples within each partition are distinguishable by a discriminator, which
is a set of attributes.
2.10 We can convert any weak entity set to a strong entity set by simply adding appropriate attributes. Why, then, do we have weak entity sets?
Answer: We have weak entities for several reasons:
• We want to avoid the data duplication and consequent possible inconsistencies caused by duplicating the key of the strong entity.
• Weak entities reflect the logical structure of an entity being dependent on
another entity.
• Weak entities can be deleted automatically when their strong entity is deleted.
• Weak entities can be stored physically with their strong entities.
2.11 Define the concept of aggregation. Give two examples of where this concept is
useful.
14
Chapter 2
Entity Relationship Model
name
employee
deadline
works−in
name
project
requires
machinery
name
Figure 2.8
E-R diagram Example 1 of aggregation.
name
tie−up−date
name
manufacturer
tie−up
distributor
distribute
product
name
Figure 2.9
E-R diagram Example 2 of aggregation.
Answer: Aggregation is an abstraction through which relationships are treated
as higher-level entities. Thus the relationship between entities A and B is treated
as if it were an entity C. Some examples of this are:
a. Employees work for projects. An employee working for a particular project
uses various machinery. See Figure 2.8
b. Manufacturers have tie-ups with distributors to distribute products. Each
tie-up has specified for it the set of products which are to be distributed. See
Figure 2.9
Exercises
address
name
name
author
URL
address
phone
URL
publisher
address
written-by
15
published-by
name
email
phone
customer
year
book
basketID
title
price
number
basket-of
ISBN
contains
shopping-basket
stocks
warehouse
number
Figure 2.10
address
code
phone
E-R diagram for Exercise 2.12.
2.12 Consider the E-R diagram in Figure 2.10, which models an online bookstore.
a. List the entity sets and their primary keys.
b. Suppose the bookstore adds music cassettes and compact disks to its collection. The same music item may be present in cassette or compact disk
format, with differing prices. Extend the E-R diagram to model this addition, ignoring the effect on shopping baskets.
c. Now extend the E-R diagram, using generalization, to model the case where
a shopping basket may contain any combination of books, music cassettes,
or compact disks.
Answer:
2.13 Consider an E-R diagram in which the same entity set appears several times.
Why is allowing this redundancy a bad practice that one should avoid whenever
possible?
Answer: By using one entity set many times we are missing relationships in
16
Chapter 2
Entity Relationship Model
ss#
name
student
ss#
takes
Figure 2.11
class
teamname
name
student
courseno
dept
plays
sport
E-R diagram with entity duplication.
the model. For example, in the E-R diagram in Figure 2.11: the students taking
classes are the same students who are athletes, but this model will not show
that.
2.14 Consider a university database for the scheduling of classrooms for final exams.
This database could be modeled as the single entity set exam, with attributes
course-name, section-number, room-number, and time. Alternatively, one or more
additional entity sets could be defined, along with relationship sets to replace
some of the attributes of the exam entity set, as
• course with attributes name, department, and c-number
• section with attributes s-number and enrollment, and dependent as a weak
entity set on course
• room with attributes r-number, capacity, and building
a. Show an E-R diagram illustrating the use of all three additional entity sets
listed.
b. Explain what application characteristics would influence a decision to include or not to include each of the additional entity sets.
Answer:
a. See Figure 2.12
b. The additional entity sets are useful if we wish to store their attributes as
part of the database. For the course entity set, we have chosen to include
three attributes. If only the primary key (c-number) were included, and if
courses have only one section, then it would be appropriate to replace the
course (and section) entity sets by an attribute (c-number) of exam. The reason
it is undesirable to have multiple attributes of course as attributes of exam is
that it would then be difficult to maintain data on the courses, particularly
if a course has no exam or several exams. Similar remarks apply to the room
entity set.
Exercises
department
name
course
s-number
17
enrollment
section of
section
for
room
in
exam
c-number
r-number
capacity
Figure 2.12
building
time
exam-id
E-R diagram for exam scheduling.
2.15 When designing an E-R diagram for a particular enterprise, you have several
alternatives from which to choose.
a. What criteria should you consider in making the appropriate choice?
b. Design three alternative E-R diagrams to represent the university registrar’s
office of Exercise 2.4. List the merits of each. Argue in favor of one of the
alternatives.
Answer:
a. The criteria to use are intuitive design, accurate expression of the real-world
concept and efficiency. A model which clearly outlines the objects and relationships in an intuitive manner is better than one which does not, because
it is easier to use and easier to change. Deciding between an attribute and
an entity set to represent an object, and deciding between an entity set and
relationship set, influence the accuracy with which the real-world concept
is expressed. If the right design choice is not made, inconsistency and/or
loss of information will result. A model which can be implemented in an
efficient manner is to be preferred for obvious reasons.
b. Consider three different alternatives for the problem in Exercise 2.4.
• See Figure 2.13
• See Figure 2.14
• See Figure 2.15
Each alternative has merits, depending on the intended use of the database.
Scheme 2.13 has been seen earlier. Scheme 2.15 does not require a separate
entity for prerequisites. However, it will be difficult to store all the prerequisites(being a multi-valued attribute). Scheme 2.14 treats prerequisites as
well as classrooms as separate entities, making it useful for gathering data
about prerequisites and room usage. Scheme 2.13 is in between the others,
in that it treats prerequisites as separate entities but not classrooms. Since a
registrar’s office probably has to answer general questions about the number of classes a student is taking or what are all the prerequisites of a course,
or where a specific class meets, scheme 2.14 is probably the best choice.
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Chapter 2
Entity Relationship Model
sid
name
student
secno
time
course−
offerings
enrols
year
iid
room
instructor
teaches
semester
name
dept
title
grade
program
is
offered
syllabus
courseno
prerequisite
requires
course
title
maincourse
credits
Figure 2.13
E-R diagram for University(a) .
room_no
building
room
ss#
student
name
time
course−
offerings
enrols
year
program
meetsin
secno
iss#
instructor
teaches
semester
name
dept
grade
is
offered
syllabus
courseno
prerequisite
requires
course
title
maincourse
credits
Figure 2.14
E-R diagram for University(b).
title
Exercises
ss#
student
name
secno
time
course−
offerings
enrols
year
program
room
iss#
name
instructor
teaches
semester
19
dept
title
grade
is
offered
syllabus
courseno
course
prerequisite
title
credits
Figure 2.15
E-R diagram for University(c).
2.16 An E-R diagram can be viewed as a graph. What do the following mean in terms
of the structure of an enterprise schema?
a. The graph is disconnected.
b. The graph is acyclic.
Answer:
a. If a pair of entity sets are connected by a path in an E-R diagram, the entity sets are related, though perhaps indirectly. A disconnected graph implies that there are pairs of entity sets that are unrelated to each other. If we
split the graph into connected components, we have, in effect, a separate
database corresponding to each connected component.
b. As indicated in the answer to the previous part, a path in the graph between
a pair of entity sets indicates a (possibly indirect) relationship between the
two entity sets. If there is a cycle in the graph then every pair of entity sets
on the cycle are related to each other in at least two distinct ways. If the E-R
diagram is acyclic then there is a unique path between every pair of entity
sets and, thus, a unique relationship between every pair of entity sets.
2.17 In Section 2.4.3, we represented a ternary relationship (Figure 2.16a) using binary relationships, as shown in Figure 2.16b. Consider the alternative shown in
Figure 2.16c. Discuss the relative merits of these two alternative representations
of a ternary relationship by binary relationships.
Answer: The model of Figure 2.16c will not be able to represent all ternary
relationships. Consider the ABC relationship set below.
20
Chapter 2
Entity Relationship Model
A
A
RA
B
R
C
B
RB
(a)
E
RC
C
(b)
R1
A
R3
B
R2
C
(c)
Figure 2.16
E-R diagram for Exercise 2.17 (attributes not shown.)
A B C
1 2 3
4 2 7
4 8 3
If ABC is broken into three relationships sets AB, BC and AC, the three will
imply that the relation (4, 2, 3) is a part of ABC.
2.18 Consider the representation of a ternary relationship using binary relationships
as described in Section 2.4.3 (shown in Figure 2.16b.)
a. Show a simple instance of E, A, B, C, RA , RB , and RC that cannot correspond to any instance of A, B, C, and R.
b. Modify the E-R diagram of Figure 2.16b to introduce constraints that will
guarantee that any instance of E, A, B, C, RA , RB , and RC that satisfies the
constraints will correspond to an instance of A, B, C, and R.
c. Modify the translation above to handle total participation constraints on the
ternary relationship.
d. The above representation requires that we create a primary key attribute for
E. Show how to treat E as a weak entity set so that a primary key attribute
is not required.
Answer:
a. Let E = {e1 , e2 }, A = {a1 , a2 }, B = {b1 }, C = {c1 }, RA = {(e1 , a1 ), (e2 , a2 )},
RB = {(e1 , b1 )}, and RC = {(e1 , c1 )}. We see that because of the tuple
(e2 , a2 ), no instance of R exists which corresponds to E, RA , RB and RC .
Exercises
21
A
RA
B
R
B
Figure 2.17
E
R
C
C
E-R diagram to Exercise 2.17b.
A
RA
B
R
B
Figure 2.18
E
R
C
C
E-R diagram to Exercise 2.17d.
b. See Figure 2.17. The idea is to introduce total participation constraints between E and the relationships RA , RB , RC so that every tuple in E has a
relationship with A, B and C.
c. Suppose A totally participates in the relationhip R, then introduce a total
participation constraint between A and RA .
d. Consider E as a weak entity set and RA , RB and RC as its identifying relationship sets. See Figure 2.18.
2.19 A weak entity set can always be made into a strong entity set by adding to its
attributes the primary key attributes of its identifying entity set. Outline what
sort of redundancy will result if we do so.
Answer: The primary key of a weak entity set can be inferred from its relationship with the strong entity set. If we add primary key attributes to the weak
entity set, they will be present in both the entity set and the relationship set and
they have to be the same. Hence there will be redundancy.
2.20 Design a generalization– specialization hierarchy for a motor-vehicle sales company. The company sells motorcycles, passenger cars, vans, and buses. Justify
your placement of attributes at each level of the hierarchy. Explain why they
should not be placed at a higher or lower level.
Answer: Figure 2.19 gives one possible hierarchy, there could be many different solutions. The generalization– specialization hierarchy for the motor-vehicle
company is given in the figure. model, sales-tax-rate and sales-volume are attributes
necessary for all types of vehicles. Commercial vehicles attract commercial vehi-
22
Chapter 2
Entity Relationship Model
model
commercialvehicle-tax-rate
sales-taxrate
sales-volume
vehicle
isa
maxpassengers
commercialvehicle
luxury-vehicletax-rate
non-commercialvehicle
isa
bus
isa
van
car
motorcycle
type
Figure 2.19
E-R diagram of motor-vehicle sales company.
cle tax, and each kind of commercial vehicle has a passenger carrying capacity
specified for it. Some kinds of non-commercial vehicles attract luxury vehicle
tax. Cars alone can be of several types, such as sports-car, sedan, wagon etc.,
hence the attribute type.
2.21 Explain the distinction between condition-defined and user-defined constraints.
Which of these constraints can the system check automatically? Explain your
answer.
Answer: In a generalization– specialization hierarchy, it must be possible to decide which entities are members of which lower level entity sets. In a conditiondefined design constraint, membership in the lower level entity-sets is evaluated on the basis of whether or not an entity satisfies an explicit condition or
predicate.User-defined lower-level entity sets are not constrained by a membership condition; rather, entities are assigned to a given entity set by the database
user.
Condition-defined constraints alone can be automatically handled by the system. Whenever any tuple is inserted into the database, its membership in the
various lower level entity-sets can be automatically decided by evaluating the
respective membership predicates. Similarly when a tuple is updated, its membership in the various entity sets can be re-evaluated automatically.
2.22 Explain the distinction between disjoint and overlapping constraints.
Answer: In a disjointness design constraint, an entity can belong to not more
Exercises
A
Figure 2.20
X
Y
ISA
ISA
B
23
C
E-R diagram for Exercise 2.24 (attributes not shown).
customer
loan
customer−id
customer−name
customer−street
customer−city
loan−number
amount
Figure 2.21
1..1 borrower
0..1
UML equivalent of Figure 2.9c.
than one lower-level entity set. In overlapping generalizations, the same entity may belong to more than one lower-level entity sets. For example, in the
employee-workteam example of the book, a manager may participate in more
than one work-team.
2.23 Explain the distinction between total and partial constraints.
Answer: In a total design constraint, each higher-level entity must belong to a
lower-level entity set. The same need not be true in a partial design constraint.
For instance, some employees may belong to no work-team.
2.24 Figure 2.20 shows a lattice structure of generalization and specialization. For
entity sets A, B, and C, explain how attributes are inherited from the higherlevel entity sets X and Y . Discuss how to handle a case where an attribute of X
has the same name as some attribute of Y .
Answer: A inherits all the attributes of X plus it may define its own attributes.
Similarly C inherits all the attributes of Y plus its own attributes. B inherits the
attributes of both X and Y. If there is some attribute name which belongs to both
X and Y, it may be referred to in B by the qualified name X.name or Y.name.
2.25 Draw the UML equivalents of the E-R diagrams of Figures 2.9c, 2.10, 2.12, 2.13
and 2.17.
Answer: See Figures 2.21 to 2.25
2.26 Consider two separate banks that decide to merge. Assume that both banks
use exactly the same E-R database schema —the one in Figure 2.22. (This assumption is, of course, highly unrealistic; we consider the more realistic case in
24
Chapter 2
Entity Relationship Model
account
account−number
0..*
balance
customer
customer−id
customer−name
customer−street
customer−city
1..1
depositor
access−date
Figure 2.22
UML equivalent of Figure 2.10
employee
employee−name 0..1 manager
employee−id
telephone−num
1..* worker
Figure 2.23
works−for
UML equivalent of Figure 2.12
job
title
level
work−job
employee
employee−name emp−work
employee−id
street
city
Figure 2.24
works−on
workid
work−branch
UML equivalent of Figure 2.13
branch
branch−name
assets
branch−city
Exercises
25
person
name
street
city
officer
employee
customer
salary
credit−rating
teller
officer−num
station−num
hrs−worked
Figure 2.25
secretary
hrs−worked
UML equivalent of Figure 2.17
Section 19.8.) If the merged bank is to have a single database, there are several
potential problems:
• The possibility that the two original banks have branches with the same
name
• The possibility that some customers are customers of both original banks
• The possibility that some loan or account numbers were used at both original banks (for different loans or accounts, of course)
For each of these potential problems, describe why there is indeed a potential
for difficulties. Propose a solution to the problem. For your solution, explain any
changes that would have to be made and describe what their effect would be on
the schema and the data.
Answer: In this example, we assume that both banks have the shared identifiers
for customers, such as the social security number. We see the general solution in
the next exercise.
Each of the problems mentioned does have potential for difficulties.
a. branch-name is the primary-key of the branch entity set. Therefore while merging the two banks’ entity sets, if both banks have a branch with the same
name, one of them will be lost.
26
Chapter 2
Entity Relationship Model
b. customers participate in the relationship sets cust-banker, borrower and depositor. While merging the two banks’ customer entity sets, duplicate tuples
of the same customer will be deleted. Therefore those relations in the three
mentioned relationship sets which involved these deleted tuples will have
to be updated. Note that if the tabular representation of a relationship set is
obtained by taking a union of the primary keys of the participating entity
sets, no modification to these relationship sets is required.
c. The problem caused by loans or accounts with the same number in both the
banks is similar to the problem caused by branches in both the banks with
the same branch-name.
To solve the problems caused by the merger, no schema changes are required.
Merge the customer entity sets removing duplicate tuples with the same socialsecurity field. Before merging the branch entity sets, prepend the old bank name
to the branch-name attribute in each tuple. The employee entity sets can be merged
directly, and so can the payment entity sets. No duplicate removal should be
performed. Before merging the loan and account entity sets, whenever there is a
number common in both the banks, the old number is replaced by a new unique
number, in one of the banks.
Next the relationship sets can be merged. Any relation in any relationship
set which involves a tuple which has been modified earlier due to the merger,
is itself modified to retain the same meaning. For example let 1611 be a loan
number common in both the banks prior to the merger, and let it be replaced by
a new unique number 2611 in one of the banks, say bank 2. Now all the relations
in borrower, loan-branch and loan-payment of bank 2 which refer to loan number
1611 will have to be modified to refer to 2611. Then the merger with bank 1’s
corresponding relationship sets can take place.
2.27 Reconsider the situation described for Exercise 2.26 under the assumption that
one bank is in the United States and the other is in Canada. As before, the
banks use the schema of Figure 2.22, except that the Canadian bank uses the
social-insurance number assigned by the Canadian government, whereas the U.S.
bank uses the social-security number to identify customers. What problems (beyond those identified in Exercise 2.24) might occur in this multinational case?
How would you resolve them? Be sure to consider both the scheme and the actual data values in constructing your answer.
Answer: This is a case in which the schemas of the two banks differ, so the
merger becomes more difficult. The identifying attribute for persons in the US is
social-security, and in Canada it is social-insurance. Therefore the merged schema
cannot use either of these. Instead we introduce a new attribute person-id, and
use this uniformly for everybody in the merged schema. No other change to the
schema is required. The values for the person-id attribute may be obtained by
several ways. One way would be to prepend a country code to the old socialsecurity or social-insurance values (“U” and “C” respectively, for instance), to
get the corresponding person-id values. Another way would be to assign fresh
numbers starting from 1 upwards, one number to each social-security and socialinsurance value in the old databases.
Exercises
27
Once this has been done, the actual merger can proceed as according to the
answer to the previous question. If a particular relationship set, say borrower, involves only US customers, this can be expressed in the merged database by specializing the entity-set customer into us-customer and canada-customer, and making only us-customer participate in the merged borrower. Similarly employee can
be specialized if needed.
C H A P T E R
3
Relational Model
This chapter presents the relational model and three relational languages. The relational model (Section 3.1) is used extensively throughout the text as is the relational
algebra (Section 3.2). The chapter also covers the tuple relational calculus (Section 3.6)
and domain relational calculus (Section 3.7) (which is the basis of the QBE language
described in Chapter 5). Classes that emphasize only SQL may omit the relational
calculus languages.
Our notation for the tuple relational calculus makes it easy to present the concept of a safe query. The concept of safety for the domain relational calculus, though
identical to that for the tuple calculus, is much more cumbersome notationally and
requires careful presentation. This consideration may suggest placing somewhat less
emphasis on the domain calculus for classes not planning to cover QBE.
Section 3.3 presents extended relational-algebra operations, such as outer-joins
and aggregates. The evolution of query languages such as SQL clearly indicates the
importance of such extended operations. Some of these operations, such as outerjoins can be expressed in the tuple/domain relational calculus, while extensions are
required for other operations, such as aggregation. We have chosen not to present
such extensions to the relational calculus, and instead restrict our attention to extensions of the algebra.
29
30
Chapter 3
Relational Model
model
address
driver-id
license
name
person
owns
driver
year
location
car
report-number
participated
date
accident
damage-amount
Figure 3.38. E-R diagram.
Exercises
3.1 Design a relational database for a university registrar’s office. The office maintains data about each class, including the instructor, the number of students
enrolled, and the time and place of the class meetings. For each student– class
pair, a grade is recorded.
Answer: Underlined attributes indicate the primary key.
student (student-id, name, program)
course (courseno, title, syllabus, credits)
course-offering (courseno, secno, year, semester, time, room)
instructor (instructor-id, name, dept, title)
enrols (student-id, courseno, secno, semester, year, grade)
teaches (courseno, secno, semester, year, instructor-id)
requires (maincourse, prerequisite)
3.2 Describe the differences in meaning between the terms relation and relation schema.
Illustrate your answer by referring to your solution to Exercise 3.1.
Answer: A relation schema is a type definition, and a relation is an instance of
that schema. For example, student (ss#, name) is a relation schema and
ss#
name
123-45-6789 Tom Jones
456-78-9123 Joe Brown
is a relation based on that schema.
3.3 Design a relational database corresponding to the E-R diagram of Figure 3.38.
Answer: The relational database schema is given below.
person (driver-id, name, address)
car (license, year, model)
accident (report-number, location, date)
owns (driver-id, license)
participated (report-number driver-id, license, damage-amount)
Exercises
31
employee (person-name, street, city)
works (person-name, company-name, salary)
company (company-name, city)
manages (person-name, manager-name)
Figure 3.39. Relational database for Exercises 3.5, 3.8 and 3.10.
3.4 In Chapter 2, we saw how to represent many-to-many, many-to-one, one-tomany, and one-to-one relationship sets. Explain how primary keys help us to
represent such relationship sets in the relational model.
Answer: Suppose the primary key of relation schema R is {Ai1 , Ai2 , ..., Ain }
and the primary key of relation schema S is {Bi1 , Bi2 , ..., Bim }. Then a relationship between the 2 sets can be represented as a tuple (Ai1 , Ai2 , ..., Ain
Bi1 , Bi2 , ..., Bim ). In a one-to-one relationship, each value on {Ai1 , Ai2 , ..., Ain }
will appear in exactly one tuple and likewise for {Bi1 , Bi2 , ..., Bim }. In a manyto-one relationship (e.g., many A - one B), each value on {Ai1 , Ai2 , ..., Ain } will
appear once, and each value on {Bi1 , Bi2 , ..., Bin } may appear many times. In a
many-to-many relationship, values on both {Ai1 , Ai2 , ..., Ain } and { Bi1 , Bi2 , ...,
Bim } will appear many times. However, in all the above cases {Ai1 , Ai2 , ..., Ain ,
Bi1 , Bi2 , ..., Bim } is a primary key, so no tuple on (Aj1 , ..., Ajn Bk1 , ..., Bkm ) will
appear more than once.
3.5 Consider the relational database of Figure 3.39, where the primary keys are underlined. Give an expression in the relational algebra to express each of the following queries:
a. Find the names of all employees who work for First Bank Corporation.
b. Find the names and cities of residence of all employees who work for First
Bank Corporation.
c. Find the names, street address, and cities of residence of all employees who
work for First Bank Corporation and earn more than $10,000 per annum.
d. Find the names of all employees in this database who live in the same city
as the company for which they work.
e. Find the names of all employees who live in the same city and on the same
street as do their managers.
f. Find the names of all employees in this database who do not work for First
Bank Corporation.
g. Find the names of all employees who earn more than every employee of
Small Bank Corporation.
h. Assume the companies may be located in several cities. Find all companies
located in every city in which Small Bank Corporation is located.
Answer:
a. Πperson-name (σcompany-name = “First Bank Corporation” (works))
b. Πperson-name, city (employee 1
(σcompany-name = “First Bank Corporation” (works)))
32
Chapter 3
Relational Model
c. Πperson-name, street, city
(σ(company-name = “First Bank Corporation” ∧ salary > 10000)
works 1 employee)
d. Πperson-name (employee 1 works 1 company)
e. Πperson-name ((employee 1 manages)
1(manager-name = employee2.person-name ∧ employee.street = employee2.street
∧ employee.city = employee2.city) (ρemployee2 (employee)))
f. The following solutions assume that all people work for exactly one company. If one allows people to appear in the database (e.g. in employee) but
not appear in works, the problem is more complicated. We give solutions for
this more realistic case later.
Πperson-name (σcompany-name = “First Bank Corporation” (works))
If people may not work for any company:
Πperson-name (employee) − Πperson-name
(σ(company-name = “First Bank Corporation”) (works))
g. Πperson-name (works) − (Πworks.person-name (works
1(works.salary ≤works2.salary ∧ works2.company-name = “Small Bank Corporation”)
ρworks2 (works)))
h. Note: Small Bank Corporation will be included in each answer.
Πcompany-name (company ÷
(Πcity (σcompany-name = “Small Bank Corporation” (company))))
3.6 Consider the relation of Figure 3.21, which shows the result of the query “Find
the names of all customers who have a loan at the bank.” Rewrite the query
to include not only the name, but also the city of residence for each customer.
Observe that now customer Jackson no longer appears in the result, even though
Jackson does in fact have a loan from the bank.
a. Explain why Jackson does not appear in the result.
b. Suppose that you want Jackson to appear in the result. How would you
modify the database to achieve this effect?
c. Again, suppose that you want Jackson to appear in the result. Write a query
using an outer join that accomplishes this desire without your having to
modify the database.
Answer: The rewritten query is
Πcustomer-name,customer-city,amount (borrower
1
loan
1
customer)
a. Although Jackson does have a loan, no address is given for Jackson in the
customer relation. Since no tuple in customer joins with the Jackson tuple of
borrower, Jackson does not appear in the result.
b. The best solution is to insert Jackson’s address into the customer relation. If
the address is unknown, null values may be used. If the database system
does not support nulls, a special value may be used (such as unknown) for
Jackson’s street and city. The special value chosen must not be a plausible
name for an actual city or street.
Exercises
c. Πcustomer-name,customer-city,amount ((borrower
1
loan)
1
33
customer)
3.7 The outer-join operations extend the natural-join operation so that tuples from
the participating relations are not lost in the result of the join. Describe how the
theta join operation can be extended so that tuples from the left, right, or both
relations are not lost from the result of a theta join.
Answer:
a. The left outer theta join of r(R) and s(S) (r 1θ s) can be defined as
(r 1θ s) ∪ ((r − ΠR (r 1θ s)) × (null, null, . . . , null))
The tuple of nulls is of size equal to the number of attributes in S.
b. The right outer theta join of r(R) and s(S) (r 1 θ s) can be defined as
(r 1θ s) ∪ ((null, null, . . . , null) × (s − ΠS (r 1θ s)))
The tuple of nulls is of size equal to the number of attributes in R.
c. The full outer theta join of r(R) and s(S) (r 1 θ s) can be defined as
(r 1θ s) ∪ ((null, null, . . . , null) × (s − ΠS (r 1θ s))) ∪
((r − ΠR (r 1θ s)) × (null, null, . . . , null))
The first tuple of nulls is of size equal to the number of attributes in R, and
the second one is of size equal to the number of attributes in S.
3.8 Consider the relational database of Figure 3.39. Give an expression in the relational algebra for each request:
Modify the database so that Jones now lives in Newtown.
Give all employees of First Bank Corporation a 10 percent salary raise.
Give all managers in this database a 10 percent salary raise.
Give all managers in this database a 10 percent salary raise, unless the salary
would be greater than $100,000. In such cases, give only a 3 percent raise.
e. Delete all tuples in the works relation for employees of Small Bank Corporation.
a.
b.
c.
d.
Answer:
a. employee ← Πperson-name,street,“N ewtown
(σperson-name=“Jones” (employee))
∪ (employee − σperson-name=“Jones” (employee))
b. works ← Πperson-name,company-name,1.1∗salary (
σ(company-name=“First Bank Corporation”) (works))
∪ (works − σcompany-name=“First Bank Corporation” (works))
c. The update syntax allows reference to a single relation only. Since this update requires access to both the relation to be updated (works) and the manages relation, we must use several steps. First we identify the tuples of works
to be updated and store them in a temporary relation (t1 ). Then we create
a temporary relation containing the new tuples (t2 ). Finally, we delete the
tuples in t1 , from works and insert the tuples of t2 .
t1 ← Πworks.person-name,company-name,salary
(σworks.person-name=manager-name (works × manages))
34
Chapter 3
Relational Model
t2 ← Πperson-name,company-name,1.1∗salary (t1 )
works ← (works − t1 ) ∪ t2
d. The same situation arises here. As before, t1 , holds the tuples to be updated
and t2 holds these tuples in their updated form.
t1 ← Πworks.person-name,company-name,salary
(σworks.person-name=manager-name (works × manages))
t2 ← Πworks.person-name,company-name,salary∗1.03
(σt1 .salary ∗ 1.1 > 100000 (t1 ))
t2 ← t2 ∪ (Πworks.person-name,company-name,salary∗1.1
(σt1 .salary ∗ 1.1 ≤ 100000 (t1 )))
works ← (works − t1 ) ∪ t2
e. works ← works − σcompany−name=“Small Bank Corporation” (works)
3.9 Using the bank example, write relational-algebra queries to find the accounts
held by more than two customers in the following ways:
a. Using an aggregate function.
b. Without using any aggregate functions.
Answer:
Gcount customer
a. t1 ← account-number
-name (depositor)
Πaccount-number σnum-holders>2 ρaccount-holders(account-number,num-holders) (t1 )
b. t1 ← (ρd1 (depositor) × ρd2 (depositor) × ρd3 (depositor))
t2 ← σ(d1.account-number=d2.account-number=d3.account-number) (t1 )
Πd1.account-number (σ(d1.customer-name=d2.customer-name ∧
d2.customer -name=d3.customer -name ∧d3.customer -name=d1.customer -name) (t2 ))
3.10 Consider the relational database of Figure 3.39. Give a relational-algebra expression for each of the following queries:
a. Find the company with the most employees.
b. Find the company with the smallest payroll.
c. Find those companies whose employees earn a higher salary, on average,
than the average salary at First Bank Corporation.
Answer:
a. t1 ← company-name Gcount-distinct person-name (works)
t2 ← maxnum-employees (ρcompany-strength(company-name,num-employees) (t1 ))
Πcompany-name (ρt3 (company-name,num-employees) (t1 ) 1 ρt4 (num-employees) (t2 ))
b. t1 ← company-name Gsum salary (works)
t2 ← minpayroll (ρcompany-payroll(company-name,payroll) (t1 ))
Πcompany-name (ρt3 (company-name,payroll) (t1 ) 1 ρt4 (payroll) (t2 ))
c. t1 ← company-name Gavg salary (works)
t2 ← σcompany-name = “First Bank Corporation” (t1 )
Exercises
35
Πt3 .company-name ((ρt3 (company-name,avg-salary) (t1 ))
1t3 .avg-salary > f irst-bank.avg-salary (ρf irst-bank(company-name,avg-salary) (t2 )))
3.11 List two reasons why we may choose to define a view.
Answer:
a. Security conditions may require that the entire logical database be not visible to all users.
b. We may wish to create a personalized collection of relations that is better
matched to a certain user’s intuition than is the actual logical model.
3.12 List two major problems with processing update operations expressed in terms
of views.
Answer: Views present significant problems if updates are expressed with them.
The difficulty is that a modification to the database expressed in terms of a view
must be translated to a modification to the actual relations in the logical model
of the database.
a. Since the view may not have all the attributes of the underlying tables, insertion of a tuple into the view will insert tuples into the underlying tables,
with those attributes not participating in the view getting null values. This
may not be desirable, especially if the attribute in question is part of the
primary key of the table.
b. If a view is a join of several underlying tables and an insertion results in
tuples with nulls in the join columns, the desired effect of the insertion will
not be achieved. In other words, an update to a view may not be expressible
at all as updates to base relations. For an explanatory example, see the loaninfo updation example in Section 3.5.2.
3.13 Let the following relation schemas be given:
R
= (A, B, C)
S
= (D, E, F )
Let relations r(R) and s(S) be given. Give an expression in the tuple relational
calculus that is equivalent to each of the following:
a.
b.
c.
d.
ΠA (r)
σB = 17 (r)
r × s
ΠA,F (σC = D (r × s))
Answer:
a. {t | ∃ q ∈ r (q[A] = t[A])}
b. {t | t ∈ r ∧ t[B] = 17}
c. {t | ∃ p ∈ r ∃ q ∈ s (t[A] = p[A] ∧ t[B] = p[B]∧ t[C] = p[C] ∧ t[D] = q[D]
∧ t[E] = q[E] ∧ t[F ] = q[F ])}
d. {t | ∃ p ∈ r ∃ q ∈ s (t[A] = p[A] ∧ t[F ] = q[F ] ∧ p[C] = q[D]}
36
Chapter 3
Relational Model
3.14 Let R = (A, B, C), and let r1 and r2 both be relations on schema R. Give
an expression in the domain relational calculus that is equivalent to each of the
following:
a.
b.
c.
d.
e.
f.
ΠA (r1 )
σB = 17 (r1 )
r1 ∪ r2
r1 ∩ r2
r1 − r2
ΠA,B (r1 ) 1 ΠB,C (r2 )
Answer:
a.
b.
c.
d.
e.
f.
{< t > | ∃ p, q (< t, p, q > ∈ r1 )}
{< a, b, c > | < a, b, c > ∈ r1 ∧ b = 17}
{< a, b, c > | < a, b, c > ∈ r1 ∨ < a, b, c > ∈ r2 }
{< a, b, c > | < a, b, c > ∈ r1 ∧ < a, b, c > ∈ r2 }
{< a, b, c > | < a, b, c > ∈ r1 ∧ < a, b, c > ∈ r2 }
{< a, b, c > | ∃ p, q (< a, b, p > ∈ r1 ∧ < q, b, c > ∈ r2 )}
3.15 Repeat Exercise 3.5 using the tuple relational calculus and the domain relational
calculus.
Answer:
a. Find the names of all employees who work for First Bank Corporation:i. {t | ∃ s ∈ works (t[person-name] = s[person-name]
∧ s[company-name] = “First Bank Corporation”)}
ii. { < p > | ∃ c, s (< p, c, s > ∈ works ∧ c = “First Bank Corporation”)}
b. Find the names and cities of residence of all employees who work for First
Bank Corporation:i. {t | ∃ r ∈ employee ∃ s ∈ works ( t[person-name] = r[person-name]
∧ t[city] = r[city] ∧ r[person-name] = s[person-name]
∧ s[company-name] = “First Bank Corporation”)}
ii. {< p, c > | ∃ co, sa, st (< p, co, sa > ∈ works
∧ < p, st, c > ∈ employee ∧ co = “First Bank Corporation”)}
c. Find the names, street address, and cities of residence of all employees who
work for First Bank Corporation and earn more than $10,000 per annum:i. {t | t ∈ employee ∧ (∃ s ∈ works ( s[person-name] = t[person-name]
∧ s[company-name] = “First Bank Corporation” ∧ s[salary] >
10000))}
ii. {< p, s, c > | < p, s, c > ∈ employee ∧ ∃ co, sa (< p, co, sa > ∈ works
∧ co = “First Bank Corporation” ∧ sa > 10000)}
d. Find the names of all employees in this database who live in the same city
as the company for which they work:i. {t | ∃ e ∈ employee ∃ w ∈ works ∃ c ∈ company
(t[person-name] = e[person-name]
∧ e[person-name] = w[person-name]
∧ w[company-name] = c[company-name] ∧ e[city] = c[city])}
Exercises
e.
f.
g.
h.
37
ii. {< p > | ∃ st, c, co, sa (< p, st, c > ∈ employee
∧ < p, co, sa > ∈ works ∧ < co, c > ∈ company)}
Find the names of all employees who live in the same city and on the same
street as do their managers:i. { t | ∃ l ∈ employee ∃ m ∈ manages ∃ r ∈ employee
(l[person-name] = m[person-name] ∧ m[manager-name] =
r[person-name]
∧ l[street] = r[street] ∧ l[city] = r[city] ∧ t[person-name] =
l[person-name])}
ii. {< t > | ∃ s, c, m (< t, s, c > ∈ employee ∧ < t, m > ∈ manages ∧ <
m, s, c > ∈ employee)}
Find the names of all employees in this database who do not work for First
Bank Corporation:If one allows people to appear in the database (e.g. in employee) but not appear in works, the problem is more complicated. We give solutions for this
more realistic case later.
i. { t | ∃ w ∈ works ( w[company-name] = “First Bank Corporation”
∧ t[person-name] = w[person-name])}
ii. { < p > | ∃ c, s (< p, c, s > ∈ works ∧ c = “First Bank Corporation”)}
If people may not work for any company:
i. { t | ∃ e ∈ employee ( t[person-name] = e[person-name] ∧ ¬ ∃ w ∈
works
(w[company-name] = “First Bank Corporation”
∧ w[person-name] = t[person-name]))}
ii. { < p > | ∃ s, c (< p, s, c > ∈ employee) ∧ ¬ ∃ x, y
(y = “First Bank Corporation”∧ < p, y, x > ∈ works)}
Find the names of all employees who earn more than every employee of
Small Bank Corporation:i. {t | ∃ w ∈ works (t[person-name] = w[person-name] ∧ ∀ s ∈ works
(s[company-name] = “Small Bank Corporation” ⇒ w[salary] >
s[salary]))}
ii. {< p > | ∃ c, s (< p, c, s > ∈ works ∧ ∀ p2 , c2 , s2
(< p2 , c2 , s2 > ∈ works ∨ c2 = “Small Bank Corporation” ∨ s >
s2 ))}
Assume the companies may be located in several cities. Find all companies
located in every city in which Small Bank Corporation is located.
Note: Small Bank Corporation will be included in each answer.
i. {t | ∀ s ∈ company (s[company-name] = “Small Bank Corporation” ⇒
∃ r ∈ company (t[company-name] = r[company-name] ∧ r[city] =
s[city]))}
ii. {< co > | ∀ co2 , ci2 (< co2 , ci2 > ∈ company
∨ co2 = “Small Bank Corporation” ∨ < co, ci2 > ∈ company)}
3.16 Let R = (A, B) and S = (A, C), and let r(R) and s(S) be relations. Write
relational-algebra expressions equivalent to the following domain-relationalcalculus expressions:
38
Chapter 3
Relational Model
a.
b.
c.
d.
{< a > | ∃ b (< a, b > ∈ r ∧ b = 17)}
{< a, b, c > | < a, b > ∈ r ∧ < a, c > ∈ s}
{< a > | ∃ b (< a, b > ∈ r) ∨ ∀ c (∃ d (< d, c > ∈ s) ⇒ < a, c > ∈ s)}
{< a > | ∃ c (< a, c > ∈ s ∧ ∃ b1 , b2 (< a, b1 > ∈ r ∧ < c, b2 >
∈ r ∧ b1 > b2 ))}
Answer:
a.
b.
c.
d.
ΠA (σB = 17 (r))
r 1 s
ΠA (r) ∪ (r ÷ σB (ΠC (s)))
Πr.A ((r 1 s) 1c = r2.A ∧ r.B > r2.B (ρr2 (r)))
It is interesting to note that (d) is an abstraction of the notorious query
“Find all employees who earn more than their manager.” Let R = (emp, sal),
S = (emp, mgr) to observe this.
3.17 Let R = (A, B) and S = (A, C), and let r(R) and s(S) be relations. Using
the special constant null, write tuple-relational-calculus expressions equivalent
to each of the following:
a. r
b. r
c. r
1s
1s
1s
Answer:
a. {t | ∃r ∈ R ∃s ∈ S (r[A] = s[A] ∧ t[A] = r[A] ∧ t[B] = r[B] ∧ t[C] = s[C]) ∨
∃s ∈ S(¬∃r ∈ R(r[A] = s[A]) ∧ t[A] = s[A] ∧ t[C] = s[C] ∧ t[B] = null)}
b. {t | ∃r ∈ R ∃s ∈ S (r[A] = s[A] ∧ t[A] = r[A] ∧ t[B] = r[B] ∧ t[C] = s[C]) ∨
∃r ∈ R(¬∃s ∈ S(r[A] = s[A]) ∧ t[A] = r[A] ∧ t[B] = r[B] ∧ t[C] = null) ∨
∃s ∈ S(¬∃r ∈ R(r[A] = s[A]) ∧ t[A] = s[A] ∧ t[C] = s[C] ∧ t[B] = null)}
c. {t | ∃r ∈ R ∃s ∈ S (r[A] = s[A] ∧ t[A] = r[A] ∧ t[B] = r[B] ∧ t[C] = s[C]) ∨
∃r ∈ R(¬∃s ∈ S(r[A] = s[A]) ∧ t[A] = r[A] ∧ t[B] = r[B] ∧ t[C] = null)}
3.18 List two reasons why null values might be introduced into the database.
Answer: Nulls may be introduced into the database because the actual value
is either unknown or does not exist. For example, an employee whose address
has changed and whose new address is not yet known should be retained with
a null address. If employee tuples have a composite attribute dependents, and
a particular employee has no dependents, then that tuple’s dependents attribute
should be given a null value.
3.19 Certain systems allow marked nulls. A marked null ⊥i is equal to itself, but if
i = j, then ⊥i = ⊥j . One application of marked nulls is to allow certain updates
through views. Consider the view loan-info (Section 3.5). Show how you can use
marked nulls to allow the insertion of the tuple (“Johnson”, 1900) through loaninfo.
Answer: To insert the tuple (“Johnson”, 1900) into the view loan-info, we can do
Exercises
the following:borrower ← (“Johnson”, ⊥k ) ∪ borrower
loan ← (⊥k , ⊥, 1900) ∪ loan
such that ⊥k is a new marked null not already existing in the database.
39
C H A P T E R
4
SQL
Chapter 4 covers the relational language SQL. The discussion is based on SQL-92,
since the more recent SQL:1999 is not widely supported yet. Extensions provided by
SQL:1999 are covered later in Chapters 9 and 22. Integrity constraint and authorization
features of SQL-92 are described in Chapter 6. SQL being a large language, many of its
features are not covered here, and are not appropriate for an introductory course on
databases. Standard books on SQL, such as Date and Darwen [1993] and Melton and
Simon [1993], or the system manuals of the database system you use can be used as
supplements for students who want to delve deeper into the intricacies of SQL.
Although it is possible to cover this chapter using only handwritten exercises, we
strongly recommend providing access to an actual database system that supports
SQL. A style of exercise we have used is to create a moderately large database and
give students a list of queries in English to write and run using SQL. We publish the
actual answers (that is the result relations they should get, not the SQL they must enter). By using a moderately large database, the probability that a “wrong” SQL query
will just happen to return the “right” result relation can be made very small. This
approach allows students to check their own answers for correctness immediately
rather than wait for grading and thereby it speeds up the learning process. A few
such example databases are available on the Web home page of this book.
Exercises that pertain to database design are best deferred until after Chapter 7.
Given the fact that the ODBC and JDBC protocols are fast becoming a primary
means of accessing databases, we have significantly extended our coverage of these
two protocols, including some examples. However, our coverage is only introductory, and omits many details that are useful in practise. Online tutorials/manuals or
textbooks covering these protocols should be used as supplements, to help students
make full use of the protocols.
Changes from 3rd edition:
Our coverage of SQL has been expanded to include the with clause, ODBC, JDBC, and
schemas, catalogs and environments (Section 4.14).
41
42
Chapter 4
SQL
Exercises
4.1 Consider the insurance database of Figure 4.12, where the primary keys are underlined. Construct the following SQL queries for this relational database.
a. Find the total number of people who owned cars that were involved in accidents in 1989.
b. Find the number of accidents in which the cars belonging to “John Smith”
were involved.
c. Add a new accident to the database; assume any values for required attributes.
d. Delete the Mazda belonging to “John Smith”.
e. Update the damage amount for the car with license number “AABB2000” in
the accident with report number “AR2197” to $3000.
Answer: Note: The participated relation relates drivers, cars, and accidents.
a. Find the total number of people who owned cars that were involved in accidents in 1989.
Note: this is not the same as the total number of accidents in 1989. We
must count people with several accidents only once.
select
from
where
and
and
count (distinct name)
accident, participated, person
accident.report-number = participated.report-number
participated.driver-id = person.driver-id
date between date ’1989-00-00’ and date ’1989-12-31’
b. Find the number of accidents in which the cars belonging to “John Smith”
were involved.
select
from
where
count (distinct *)
accident
exists
(select *
from participated, person
where participated.driver-id = person.driver-id
and person.name = ’John Smith’
and accident.report-number = participated.report-number)
c. Add a new accident to the database; assume any values for required attributes.
We assume the driver was “Jones,” although it could be someone else.
Also, we assume “Jones” owns one Toyota. First we must find the license of
the given car. Then the participated and accident relations must be updated
in order to both record the accident and tie it to the given car. We assume
values “Berkeley” for location, ’2001-09-01’ for date and date, 4007 for reportnumber and 3000 for damage amount.
Exercises
43
person (driver-id, name, address)
car (license, model, year)
accident (report-number, date, location)
owns (driver-id, license)
participated (driver-id, car, report-number, damage-amount)
Figure 4.12. Insurance database.
insert into accident
values (4007, ’2001-09-01’, ’Berkeley’)
insert into participated
select o.driver-id, c.license, 4007, 3000
from person p, owns o, car c
where p.name = ’Jones’ and p.driver-id = o.driver-id and
o.license = c.license and c.model = ’Toyota’
d. Delete the Mazda belonging to “John Smith”.
Since model is not a key of the car relation, we can either assume that only
one of John Smith’s cars is a Mazda, or delete all of John Smith’s Mazdas
(the query is the same). Again assume name is a key for person.
delete car
where model = ’Mazda’ and license in
(select license
from person p, owns o
where p.name = ’John Smith’ and p.driver-id = o.driver-id)
Note: The owns, accident and participated records associated with the Mazda
still exist.
e. Update the damage amount for the car with license number “AABB2000” in
the accident with report number “AR2197” to $3000.
update participated
set damage-amount = 3000
where report-number = “AR2197” and driver-id in
(select driver-id
from owns
where license = “AABB2000”)
4.2 Consider the employee database of Figure 4.13, where the primary keys are underlined. Give an expression in SQL for each of the following queries.
a. Find the names of all employees who work for First Bank Corporation.
b. Find the names and cities of residence of all employees who work for First
Bank Corporation.
c. Find the names, street addresses, and cities of residence of all employees
who work for First Bank Corporation and earn more than $10,000.
44
Chapter 4
SQL
d. Find all employees in the database who live in the same cities as the companies for which they work.
e. Find all employees in the database who live in the same cities and on the
same streets as do their managers.
f. Find all employees in the database who do not work for First Bank Corporation.
g. Find all employees in the database who earn more than each employee of
Small Bank Corporation.
h. Assume that the companies may be located in several cities. Find all companies located in every city in which Small Bank Corporation is located.
i. Find all employees who earn more than the average salary of all employees
of their company.
j. Find the company that has the most employees.
k. Find the company that has the smallest payroll.
l. Find those companies whose employees earn a higher salary, on average,
than the average salary at First Bank Corporation.
Answer:
a. Find the names of all employees who work for First Bank Corporation.
select employee-name
from works
where company-name = ’First Bank Corporation’
b. Find the names and cities of residence of all employees who work for First
Bank Corporation.
select e.employee-name, city
from employee e, works w
where w.company-name = ’First Bank Corporation’ and
w.employee-name = e.employee-name
c. Find the names, street address, and cities of residence of all employees who
work for First Bank Corporation and earn more than $10,000.
If people may work for several companies, the following solution will
only list those who earn more than $10,000 per annum from “First Bank
Corporation” alone.
select *
from employee
where employee-name in
(select employee-name
from works
where company-name = ’First Bank Corporation’ and salary ¿ 10000)
As in the solution to the previous query, we can use a join to solve this one
also.
d. Find all employees in the database who live in the same cities as the companies for which they work.
Exercises
45
select e.employee-name
from employee e, works w, company c
where e.employee-name = w.employee-name and e.city = c.city and
w.company -name = c.company -name
e. Find all employees in the database who live in the same cities and on the
same streets as do their managers.
select P.employee-name
from employee P, employee R, manages M
where P.employee-name = M.employee-name and
M.manager-name = R.employee-name and
P.street = R.street and P.city = R.city
f. Find all employees in the database who do not work for First Bank Corporation.
The following solution assumes that all people work for exactly one company.
select employee-name
from works
where company-name = ’First Bank Corporation’
If one allows people to appear in the database (e.g. in employee) but not
appear in works, or if people may have jobs with more than one company,
the solution is slightly more complicated.
select employee-name
from employee
where employee-name not in
(select employee-name
from works
where company-name = ’First Bank Corporation’)
g. Find all employees in the database who earn more than every employee of
Small Bank Corporation.
The following solution assumes that all people work for at most one company.
select employee-name
from works
where salary > all
(select salary
from works
where company-name = ’Small Bank Corporation’)
If people may work for several companies and we wish to consider the
total earnings of each person, the problem is more complex. It can be solved
by using a nested subquery, but we illustrate below how to solve it using
the with clause.
46
Chapter 4
SQL
with emp-total-salary as
(select employee-name, sum(salary) as total-salary
from works
group by employee-name
)
select employee-name
from emp-total-salary
where total-salary > all
(select total-salary
from emp-total-salary, works
where works.company-name = ’Small Bank Corporation’ and
emp-total-salary.employee-name = works.employee-name
)
h. Assume that the companies may be located in several cities. Find all companies located in every city in which Small Bank Corporation is located.
The simplest solution uses the contains comparison which was included
in the original System R Sequel language but is not present in the subsequent SQL versions.
select T.company-name
from company T
where (select R.city
from company R
where R.company-name = T.company-name)
contains
(select S.city
from company S
where S.company-name = ’Small Bank Corporation’)
Below is a solution using standard SQL.
select S.company-name
from company S
where not exists ((select city
from company
where company-name = ’Small Bank Corporation’)
except
(select city
from company T
where S.company-name = T.company-name))
i. Find all employees who earn more than the average salary of all employees
of their company.
The following solution assumes that all people work for at most one company.
Exercises
47
employee (employee-name, street, city)
works (employee-name, company-name, salary)
company (company-name, city)
manages (employee-name, manager-name)
Figure 4.13. Employee database.
select employee-name
from works T
where salary > (select avg (salary)
from works S
where T.company-name = S.company-name)
j. Find the company that has the most employees.
select company-name
from works
group by company-name
having count (distinct employee-name) >= all
(select count (distinct employee-name)
from works
group by company-name)
k. Find the company that has the smallest payroll.
select company-name
from works
group by company-name
having sum (salary) <= all (select sum (salary)
from works
group by company-name)
l. Find those companies whose employees earn a higher salary, on average,
than the average salary at First Bank Corporation.
select company-name
from works
group by company-name
having avg (salary) > (select avg (salary)
from works
where company-name = ’First Bank Corporation’)
4.3 Consider the relational database of Figure 4.13. Give an expression in SQL for
each of the following queries.
a.
b.
c.
d.
Modify the database so that Jones now lives in Newtown.
Give all employees of First Bank Corporation a 10 percent raise.
Give all managers of First Bank Corporation a 10 percent raise.
Give all managers of First Bank Corporation a 10 percent raise unless the
salary becomes greater than $100,000; in such cases, give only a 3 percent
raise.
48
Chapter 4
SQL
e. Delete all tuples in the works relation for employees of Small Bank Corporation.
Answer: The solution for part 0.a assumes that each person has only one tuple in
the employee relation. The solutions to parts 0.c and 0.d assume that each person
works for at most one company.
a. Modify the database so that Jones now lives in Newtown.
update employee
set city = ’Newton’
where person-name = ’Jones’
b. Give all employees of First Bank Corporation a 10-percent raise.
update works
set salary = salary * 1.1
where company-name = ’First Bank Corporation’
c. Give all managers of First Bank Corporation a 10-percent raise.
update works
set salary = salary * 1.1
where employee-name in (select manager-name
from manages)
and company-name = ’First Bank Corporation’
d. Give all managers of First Bank Corporation a 10-percent raise unless the
salary becomes greater than $100,000; in such cases, give only a 3-percent
raise.
update works T
set T.salary = T.salary * 1.03
where T.employee-name in (select manager-name
from manages)
and T.salary * 1.1 > 100000
and T.company-name = ’First Bank Corporation’
update works T
set T.salary = T.salary * 1.1
where T.employee-name in (select manager-name
from manages)
and T.salary * 1.1 <= 100000
and T.company-name = ’First Bank Corporation’
SQL-92 provides a case operation (see Exercise 4.11), using which we give
a more concise solution:-
Exercises
49
update works T
set T.salary = T.salary ∗
(case
when (T.salary ∗ 1.1 > 100000) then 1.03
else 1.1
)
where T.employee-name in (select manager-name
from manages) and
T.company-name = ’First Bank Corporation’
e. Delete all tuples in the works relation for employees of Small Bank Corporation.
delete works
where company-name = ’Small Bank Corporation’
4.4 Let the following relation schemas be given:
R = (A, B, C)
S = (D, E, F )
Let relations r(R) and s(S) be given. Give an expression in SQL that is equivalent
to each of the following queries.
a.
b.
c.
d.
ΠA (r)
σB = 17 (r)
r × s
ΠA,F (σC = D (r × s))
Answer:
a. ΠA (r)
select distinct A
from r
b. σB = 17 (r)
select *
from r
where B = 17
c. r × s
select distinct *
from r, s
d. ΠA,F (σC = D (r × s))
select distinct A, F
from r, s
where C = D
4.5 Let R = (A, B, C), and let r1 and r2 both be relations on schema R. Give an
expression in SQL that is equivalent to each of the following queries.
a. r1 ∪ r2
b. r1 ∩ r2
50
Chapter 4
SQL
c. r1 − r2
d. ΠAB (r1 )
1
ΠBC (r2 )
Answer:
a. r1 ∪ r2
(select *
from r1)
union
(select *
from r2)
b. r1 ∩ r2
We can write this using the intersect operation, which is the preferred
approach, but for variety we present an solution using a nested subquery.
select *
from r1
where (A, B, C) in (select *
from r2)
c. r1 − r2
select ∗
from r1
where (A, B, C) not in (select ∗
from r2)
This can also be solved using the except clause.
d. ΠAB (r1 ) 1 ΠBC (r2 )
select r1.A, r2.B, r3.C
from r1, r2
where r1.B = r2.B
4.6 Let R = (A, B) and S = (A, C), and let r(R) and s(S) be relations. Write an
expression in SQL for each of the queries below:
a. {< a > | ∃ b (< a, b > ∈ r ∧ b = 17)}
b. {< a, b, c > | < a, b > ∈ r ∧ < a, c > ∈ s}
c. {< a > | ∃ c (< a, c > ∈ s ∧ ∃ b1 , b2 (< a, b1 > ∈ r ∧ < c, b2 > ∈ r ∧ b1 >
b2 ))}
Answer:
a. {< a > | ∃ b (< a, b > ∈ r ∧ b = 17)}
select distinct A
from r
where B = 17
b. {< a, b, c > | < a, b > ∈ r ∧ < a, c > ∈ s)}
Exercises
51
select distinct r.A, r.B, s.C
from r, s
where r.A = s.A
c. {< a > | ∃ c (< a, c > ∈ s ∧ ∃ b1 , b2 (< a, b1 > ∈ r ∧ < c, b2 > ∈ r ∧ b1 >
b2 ))}
select distinct s.A
from s, r e, r m
where s.A = e.A and s.C = m.A and e.B > m.B
4.7 Show that, in SQL, <> all is identical to not in.
Answer: Let the set S denote the result of an SQL subquery. We compare (x <>
all S) with (x not in S). If a particular value x1 satisfies (x1 <> all S) then for
all elements y of S x1 = y. Thus x1 is not a member of S and must satisfy (x1 not
in S). Similarly, suppose there is a particular value x2 which satisfies (x2 not in
S). It cannot be equal to any element w belonging to S, and hence (x2 <> all S)
will be satisfied. Therefore the two expressions are equivalent.
4.8 Consider the relational database of Figure 4.13. Using SQL, define a view consisting of manager-name and the average salary of all employees who work for
that manager. Explain why the database system should not allow updates to be
expressed in terms of this view.
Answer:
create view salinfo as
select manager-name, avg(salary)
from manages m, works w
where m.employee-name = w.employee-name
group by manager-name
Updates should not be allowed in this view because there is no way to determine how to change the underlying data. For example, suppose the request
is “change the average salary of employees working for Smith to $200”. Should
everybody who works for Smith have their salary changed to $200? Or should
the first (or more, if necessary) employee found who works for Smith have
their salary adjusted so that the average is $200? Neither approach really makes
sense.
4.9 Consider the SQL query
select p.a1
from p, r1, r2
where p.a1 = r1.a1 or p.a1 = r2.a1
Under what conditions does the preceding query select values of p.a1 that are
either in r1 or in r2? Examine carefully the cases where one of r1 or r2 may be
empty.
Answer: The query selects those values of p.a1 that are equal to some value of
r1.a1 or r2.a1 if and only if both r1 and r2 are non-empty. If one or both of r1 and
52
Chapter 4
SQL
r2 are empty, the cartesian product of p, r1 and r2 is empty, hence the result of
the query is empty. Of course if p itself is empty, the result is as expected, i.e.
empty.
4.10 Write an SQL query, without using a with clause, to find all branches where
the total account deposit is less than the average total account deposit at all
branches,
a. Using a nested query in the from clauser.
b. Using a nested query in a having clause.
Answer: We output the branch names along with the total account deposit at
the branch.
a. Using a nested query in the from clauser.
select branch-name, tot-balance
from (select branch-name, sum (balance)
from account
group by branch-name) as branch-total(branch-name, tot-balance)
where tot-balance ¡
( select avg (tot-balance)
from ( select branch-name, sum (balance)
from account
group by branch-name) as branch-total(branch-name, tot-balance)
)
b. Using a nested query in a having clause.
select branch-name, sum (balance)
from account
group by branch-name
having sum (balance) ¡
( select avg (tot-balance)
from ( select branch-name, sum (balance)
from account
group by branch-name) as branch-total(branch-name, tot-balance)
)
4.11 Suppose that we have a relation marks(student-id, score) and we wish to assign
grades to students based on the score as follows: grade F if score < 40, grade C
if 40 ≤ score < 60, grade B if 60 ≤ score < 80, and grade A if 80 ≤ score. Write
SQL queries to do the following:
a. Display the grade for each student, based on the marks relation.
b. Find the number of students with each grade.
Answer: We use the case operation provided by SQL-92:
a. To display the grade for each student:
Exercises
53
select student-id,
(case
when score < 40 then ’F’,
when score < 60 then ’C’,
when score < 80 then ’B’,
else ’A’
end) as grade
from marks
b. To find the number of students with each grade we use the following query, where
grades is the result of the query given as the solution to part 0.a.
select grade, count(student-id)
from grades
group by grade
4.12 SQL-92 provides an n-ary operation called coalesce, which is defined as follows:
coalesce(A1, A2 , . . . , An ) returns the first nonnull Ai in the list A1 , A2 , . . . , An ,
and returns null if all of A1 , A2 , . . . , An are null. Show how to express the coalesce operation using the case operation.
Answer:
case
when A1 is not null then A1
when A2 is not null then A2
...
when An is not null then An
else null
end
4.13 Let a and b be relations with the schemas A(name, address, title) and B(name, address, salary), respectively. Show how to express a natural full outer join b using
the full outer join operation with an on condition and the coalesce operation.
Make sure that the result relation does not contain two copies of the attributes
name and address, and that the solution is correct even if some tuples in a and b
have null values for attributes name or address.
Answer:
select coalesce(a.name, b.name) as name,
coalesce(a.address, b.address) as address,
a.title,
b.salary
from a full outer join b on a.name = b.name and
a.address = b.address
4.14 Give an SQL schema definition for the employee database of Figure 4.13. Choose
an appropriate domain for each attribute and an appropriate primary key for
each relation schema.
Answer:
create domain
company-names char(20)
54
Chapter 4
SQL
create domain
create domain
city-names char(30)
person-names char(20)
create table
(employee-name
street
city
primary key
employee
person-names,
char(30),
city-names,
(employee-name))
create table
(employee-name
company-name
salary
primary key
works
person-names,
company-names,
numeric(8, 2),
(employee-name))
create table
(company-name
city
primary key
company
company-names,
city-names,
(company-name))
create table
(employee-name
manager-name
primary key
manages
person-names,
person-names,
(employee-name))
4.15 Write check conditions for the schema you defined in Exercise 4.14 to ensure
that:
a. Every employee works for a company located in the same city as the city in
which the employee lives.
b. No employee earns a salary higher than that of his manager.
Answer:
a. check condition for the works table:check((employee-name, company-name) in
(select e.employee-name, c.company-name
from employee e, company c
where e.city = c.city
)
)
b. check condition for the works table:-
Exercises
55
check(
salary < all
(select manager-salary
from (select manager-name, manages.employee-name as emp-name,
salary as manager-salary
from works, manages
where works.employee-name = manages.manager-name)
where employee-name = emp-name
)
)
The solution is slightly complicated because of the fact that inside the select expression’s scope, the outer works relation into which the insertion is
being performed is inaccessible. Hence the renaming of the employee-name
attribute to emp-name. Under these circumstances, it is more natural to use
assertions, which are introduced in Chapter 6.
4.16 Describe the circumstances in which you would choose to use embedded SQL
rather than SQL alone or only a general-purpose programming language.
Answer: Writing queries in SQL is typically much easier than coding the same
queries in a general-purpose programming language. However not all kinds of
queries can be written in SQL. Also nondeclarative actions such as printing a
report, interacting with a user, or sending the results of a query to a graphical
user interface cannot be done from within SQL. Under circumstances in which
we want the best of both worlds, we can choose embedded SQL or dynamic
SQL, rather than using SQL alone or using only a general-purpose programming
language.
Embedded SQL has the advantage of programs being less complicated since it
avoids the clutter of the ODBC or JDBC function calls, but requires a specialized
preprocessor.
C H A P T E R
5
Other Relational Languages
In this chapter we study two additional relational languages, QBE and Datalog. QBE,
based on the domain relational calculus, forms the basis for query languages supported by a large number of database systems designed for personal computers, such
as Microsoft Access, FoxPro, etc. Unfortunately there is no standard for QBE; our coverage is based on the original description of QBE. The description here will have to
be supplemented by material from the user guides of the specific database system
being used. One of the points to watch out for is the precise semantics of aggregate
operations, which is particularly non-standard.
The Datalog language has several similarities to Prolog, which some students may
have studied in other courses. Datalog differs from Prolog in that its semantics is
purely declarative, as opposed to the operational semantics of Prolog. It is important
to emphasize the differences, since the declarative semantics enables the use of efficient query evaluation strategies. There are several implementations of Datalog available in the public domain, such as the Coral system from the University of Wisconsin
– Madison, and XSB from the State University of New York, Stony Brook, which can
be used for programming exercises. The Coral system also supports complex objects
such as nested relations (covered later in Chapter 9). See the Tools section at the end
of Chapter 5 for the URLs of these systems.
Changes from 3rd edition:
The syntax and semantics of QBE aggregation and update have been changed to
simplify the semantics and to remove some ambiguities in the earlier semantics. The
version of QBE supported by Microsoft Access has been covered briefly. Quel has
been dropped.
57
58
Chapter 5
Other Relational Languages
Exercises
5.1 Consider the insurance database of Figure 5.14, where the primary keys are underlined. Construct the following QBE queries for this relational-database.
a. Find the total number of people who owned cars that were involved in accidents in 1989.
b. Find the number of accidents in which the cars belonging to “John Smith”
were involved.
c. Add a new accident to the database; assume any values for required attributes.
d. Delete the Mazda belonging to “John Smith.”
e. Update the damage amount for the car with license number “AABB2000” in
the accident with report number “AR2197” to $3000.
Answer: The participated relation relates car(s) and accidents. Assume the date
attribute is of the form “YYYY-MM-DD”.
a. Find the total number of people who owned cars that were involved in accidents in 1989.
accident report-number date location
report
date
participated
driver-id
car report-number damage-amount
P.CNT.UNQ.ALL
report
conditions
date =
( ≥ 1989-00-00 and
≤ 1989-12-31 )
b. Find the number of accidents in which the cars belonging to “John Smith”
were involved.
person driver-id
name
address
driver John Smith
participated driver-id car report-number damage-amount
driver
P.CNT.ALL
c. Add a new accident to the database; assume any values for required attributes.
We assume that the driver was “Williams”, although it could have been
someone else. Also assume that “Williams” has only one Toyota.
accident
I.
report-number
date
location
4007
1997-01-01 Berkeley
Exercises
59
person (driver-id, name, address)
car (license, model, year)
accident (report-number, date, location)
owns (driver-id, license)
participated (driver-id, car, report-number, damage-amount)
Figure 5.14. Insurance database.
participated driver-id
I.
driver
car
license
report-number damage-amount
4007
3000
owns driver-id
driver
car
license
license
license
license
year model
year Toyota
person
driver-id
name
address
driver Williams
d. Delete the car “Mazda” that belongs to “John Smith.”
person
driver-id
name
driver John Smith
owns driver-id
driver
address
license
license
car license year model
D. license
Mazda
e. Update the damage amount for the car with license number “AABB2000” in
the accident with report number “AR2197” to $3000.
owns driver-id
license
driver “AABB2000”
participated driver-id car report-number damage-amount
driver
“AR2197”
U.3000
5.2 Consider the employee database of Figure 5.15. Give expressions in QBE, and
Datalog for each of the following queries:
a. Find the names of all employees who work for First Bank Corporation.
60
Chapter 5
Other Relational Languages
b. Find the names and cities of residence of all employees who work for First
Bank Corporation.
c. Find the names, street addresses, and cities of residence of all employees
who work for First Bank Corporation and earn more than $10,000 per annum.
d. Find all employees who live in the same city as the company for which they
work is located.
e. Find all employees who live in the same city and on the same street as their
managers.
f. Find all employees in the database who do not work for First Bank Corporation.
g. Find all employees who earn more than every employee of Small Bank Corporation.
h. Assume that the companies may be located in several cities. Find all companies located in every city in which Small Bank Corporation is located.
Answer:
a. Find the names of all employees who work for First Bank Corporation.
i.
works
person-name
company-name
P. x
First Bank Corporation
ii. query(X) :- works(X, “First Bank Corporation”, Y)
salary
b. Find the names and cities of residence of all employees who work for First
Bank Corporation.
i.
works
person-name
company-name
salary
x
First Bank Corporation
employee person-name street city
P. x
P. y
ii. query (X, Y ) :- employee (X, Z, Y ), works (X, “First Bank Corporation”, W )
c. Find the names, street addresses, and cities of residence of all employees
who work for First Bank Corporation and earn more than $10,000 per annum.
If people may work for several companies, the following solutions will
only list those who earn more than $10,000 per annum from “First Bank
Corporation” alone.
i.
employee person-name street city
P. x
P. y
P. z
Exercises
works
person-name
x
company-name
First Bank Co
61
salary
> 10000
ii.
query (X, Y, Z) :- lives (X, Y, Z), works (X, “First Bank Corporation”, W ),
W > 10000
d. Find all employees who live in the city where the company for which they
work is located.
i.
employee person-name street city
P. x
y
works
person-name company-name salary
x
c
company
company-name city
c
y
ii. query (X) :- employee (X, Y, Z), works (X, V, W ), company (V, Z)
e. Find all employees who live in the same city and on the same street as their
managers.
i.
employee person-name street city
P. x
s
c
y
s
c
manages person-name manager − name
x
y
ii. query (X) :- lives (X, Y, Z), manages (X, V ), lives (V, Y, Z)
f. Find all employees in the database who do not work for First Bank Corporation.
The following solutions assume that all people work for exactly one company.
i.
works
person-name company-name salary
P. x
¬ First Bank Co
ii. query (X) :- works (X, Y, Z), Y = “First Bank Corporation”
If one allows people to appear in the database (e.g. in employee) but not
appear in works, or if people may have jobs with more than one company,
the solutions are slightly more complicated. They are given below :-
62
Chapter 5
Other Relational Languages
i.
employee person-name street city
P. x
works
¬
ii.
person-name
company-name
x
First Bank Corporation
salary
query (X) :- employee (X, Y, Z), ¬ p1 (X)
p1 (X) :- works(X, “First Bank Corporation”, W )
g. Find all employees who earn more than every employee of Small Bank Corporation.
The following solutions assume that all people work for at most one company.
i.
works
person-name
company-name
Small Bank Co
P. x
salary
y
> MAX.ALL. y
or
works
¬
person-name
P. x
company-name salary
y
Small Bank Co
> y
ii.
query (X) :- works (X, Y, Z), ¬ p (X)
p (X) :- works(X, C, Y 1), works (V, “Small Bank Corporation”, Y ), Y > Y 1
h. Assume that the companies may be located in several cities. Find all companies located in every city in which Small Bank Corporation is located.
Note: Small Bank Corporation will be included in each answer.
i.
located-in
company-name
Small Bank Corporation
P. c
Small Bank Corporation
conditions
CNT.ALL. y =
CNT.ALL. x
ii.
city
x
y
y
Exercises
63
query(X) :- company(X, C), not p(X)
p(X) :- company(X, C1), company(“Small Bank Corporation”, C2), not company(X, C2)
5.3 Consider the relational database of Figure 5.15. where the primary keys are underlined. Give expressions in QBE for each of the following queries:
a. Find all employees who earn more than the average salary of all employees
of their company.
b. Find the company that has the most employees.
c. Find the company that has the smallest payroll.
d. Find those companies whose employees earn a higher salary, on average,
than the average salary at First Bank Corporation.
Answer:
a. Find all employees who earn more than the average salary of all employees
of their company.
The following solution assumes that all people work for at most one company.
works
person-name company-name salary
P.
y
x
y
z
conditions
x > AVG.ALL. z
b. Find the company that has the most employees.
works
person-name company-name salary
x
P.G.
y
G.
conditions
CNT.UNQ. x ≥ MAX.CNT.UNQ.ALL. y
c. Find the company that has the smallest payroll.
employee (person-name, street, city)
works (person-name, company-name, salary)
company (company-name, city)
manages (person-name, manager-name)
Figure 5.15. Employee database.
64
Chapter 5
Other Relational Languages
works
person-name company-name salary
P.G.
x
G.
y
conditions
SUM.ALL. x ≤ MIN.SUM.ALL. y
d. Find those companies whose employees earn a higher salary, on average,
than the average salary at First Bank Corporation.
works
person-name
company-name
salary
P.G.
x
First Bank Corporation
y
conditions
AVG.ALL. x > AVG.ALL. y
5.4 Consider the relational database of Figure 5.15. Give expressions in QBE for each
of the following queries:
Modify the database so that Jones now lives in Newtown.
Give all employees of First Bank Corporation a 10 percent raise.
Give all managers in the database a 10 percent raise.
Give all managers in the database a 10 percent raise, unless the salary would
be greater than $100,000. In such cases, give only a 3 percent raise.
e. Delete all tuples in the works relation for employees of Small Bank Corporation.
a.
b.
c.
d.
Answer: The solutions assume that each person has only one tuple in the employee relation. The solutions to parts 0.c and 0.d assume that each person works
for at most one company.
a. Modify the database so that Jones now lives in Newtown.
employee person-name street
city
Jones
U.Newtown
b. Give all employees of First Bank Corporation a 10-percent raise.
works
person-name
company-name
First Bank Corporation
U.
c. Give all managers in the database a 10-percent raise.
manages person-name manager-name
x
salary
x
x * 1.1
Exercises
works
65
person-name company-name
x
salary
y
U.
y * 1.1
d. Give all managers in the database a 10-percent raise, unless the salary would
be greater than $100,000. In such cases, give only a 3-percent raise. Two
separate update operations must be performed. Each update operation has
its own set of skeleton tables.
First update:
manages person-name manager-name
x
works
person-name company-name
x
U.
salary
y
y * 1.03
conditions
y > 100000/1.1
Second update:
manages person-name manager-name
x
works
person-name
x
company-name
U.
salary
y
y * 1.1
conditions
y ≤ 100000/1.1
e. Delete all tuples in the works relation for employees of Small Bank Corporation.
works person-name company-name salary
D.
Small Bank Co
5.5 Let the following relation schemas be given:
R = (A, B, C)
S = (D, E, F )
Let relations r(R) and s(S) be given. Give expressions in QBE, and Datalog equivalent to each of the following queries:
a. ΠA (r)
b. σB = 17 (r)
c. r × s
66
Chapter 5
Other Relational Languages
d. ΠA,F (σC = D (r × s))
Answer:
a. ΠA (r)
i.
r
A B
P.
r
P.
A
C
ii. query (X) :- r (X, Y, Z)
b. σB = 17 (r)
i.
B C
17
ii. query (X, Y, Z) :- r (X, Y, Z), Y = 17
c. r × s
i.
result
P.
A
a
B
b
C
c
D
d
r
A
a
B
b
C
c
s
D
d
E
e
F
f
E
e
F
f
ii. query (X, Y, Z, U, V, W ) :- r (X, Y, Z), s (U, V, W )
d. ΠA,F (σC = D (r × s))
i.
result
P.
A
a
F
f
r
A
a
B
C
c
s
D
c
E
F
f
ii. query (X, Y ) :- r (X, V, W ), s (W, Z, Y )
Exercises
67
5.6 Let R = (A, B, C), and let r1 and r2 both be relations on schema R. Give expressions in QBE, and Datalog equivalent to each of the following queries:
a.
b.
c.
d.
r1 ∪ r2
r1 ∩ r2
r1 − r2
ΠAB (r1 )
1
ΠBC (r2 )
Answer:
a. r1 ∪ r2
i.
result
P.
P.
ii.
A
a
d
B
b
e
r1
A
a
r2
A B
d e
C
c
f
B C
b c
C
f
query(X, Y, Z) :- r1 (X, Y, Z)
query(X, Y, Z) :- r2 (X, Y, Z)
b. r1 ∩ r2
i.
r1
P.
A
a
B C
b c
r2
A
a
B
b
C
c
ii. query(X, Y, Z) :- r1 (X, Y, Z), r2 (X, Y, Z)
c. r1 − r2
i.
r1
P.
A
a
B C
b c
68
Chapter 5
Other Relational Languages
r2
¬
A
a
B
b
C
c
ii. query(X, Y, Z) :- r1 (X, Y, Z), not r2 (X, Y, Z)
d. ΠAB (r1 )
i.
1
ΠBC (r2 )
result
P.
A
a
B
b
C
c
r1
A
a
B
b
C
r2
A
B
b
C
c
ii. query(X, Y, Z) :- r1 (X, Y, V), r2 (W, Y, Z)
5.7 Let R = (A, B) and S = (A, C), and let r(R) and s(S) be relations. Write expressions in QBE and Datalog for each of the following queries:
a. {< a > | ∃ b (< a, b > ∈ r ∧ b = 17)}
b. {< a, b, c > | < a, b > ∈ r ∧ < a, c > ∈ s}
c. {< a > | ∃ c (< a, c > ∈ s ∧ ∃ b1 , b2 (< a, b1 > ∈ r ∧ < c, b2 > ∈ r ∧ b1 >
b2 ))}
Answer:
a. {< a > | ∃ b (< a, b > ∈ r ∧ b = 17)}
i.
r
A B
P. 17
ii. query (X) :- r (X, 17)
b. {< a, b, c > | < a, b > ∈ r ∧ < a, c > ∈ s}
i.
r
A
a
B
b
Exercises
s
A
a
69
C
c
result A B C
P.
a b c
ii. query(X, Y, Z) :- r(X, Y), s(X, Z)
c. {< a > | ∃ c (< a, c > ∈ s ∧ ∃ b1 , b2 (< a, b1 > ∈ r ∧ < c, b2 > ∈ r ∧ b1 >
b2 ))}
i.
r
A
a
c
s
A
P. a
B
> s
s
C
c
ii. query (X) :- s (X, Y ), r (X, Z), r (Y, W ), Z > W
5.8 Consider the relational database of Figure 5.15. Write a Datalog program for
each of the following queries:
a. Find all employees who work (directly or indirectly) under the manager
“Jones”.
b. Find all cities of residence of all employees who work (directly or indirectly)
under the manager “Jones”.
c. Find all pairs of employees who have a (direct or indirect) manager in common.
d. Find all pairs of employees who have a (direct or indirect) manager in common, and are at the same number of levels of supervision below the common manager.
Answer:
a. Find all employees who work (directly or indirectly) under the manager
“Jones”.
query (X) :- p (X)
p (X) :- manages (X, “Jones”)
p (X) :- manages (X, Y ), p (Y )
b. Find all cities of residence of all employees who work (directly or indirectly)
under the manager “Jones”.
query(X, C) :- p(X), employee(X, S, C)
p(X) :- manages(X, “Jones”)
p(X) :- manages(X, Y), p(Y)
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Chapter 5
Other Relational Languages
c. Find all pairs of employees who have a (direct or indirect) manager in common.
query(X, Y) :- p(X, W), p(Y, W)
p(X, Y) :- manages(X, Y)
p(X, Y) :- manages(X, Z), p(Z, Y)
d. Find all pairs of employees who have a (direct or indirect) manager in common, and are at the same number of levels of supervision below the common manager.
query(X, Y) :- p(X, Y)
p(X, Y) :- manages(X, Z), manages(Y, Z)
p(X, Y) :- manages(X, V), manages(Y, W), p(V, W)
5.9 Write an extended relational-algebra view equivalent to the Datalog rule
p(A, C, D) :– q1 (A, B), q2 (B, C), q3 (4, B), D = B + 1 .
Answer: Let us assume that q1, q2 and q3 are instances of the schema (A1, A2).
The relational algebra view is
create view P as
Πq1.A1,q2.A2,q1.A2+1 (σq3.A1=4 ∧ q1.A2=q2.A1 ∧ q1.A2=q3.A2 (q1 × q2 × q3))
5.10 Describe how an arbitrary Datalog rule can be expressed as an extended relationalalgebra view.
Answer: A Datalog rule has two parts, the head and the body. The body is a
comma separated list of literals. A positive literal has the form p(t1 , t2 , . . . , tn )
where p is the name of a relation with n attributes, and t1 , t2 , . . . , tn are either
constants or variables. A negative literal has the form ¬p(t1 , t2 , . . . , tn ) where p
has n attributes. In the case of arithmetic literals, p will be an arithmetic operator
like >, = etc.
We consider only safe rules; see Section 5.2.4 for the definition of safety of
Datalog rules. Further, we assume that every variable that occurs in an arithmetic literal also occurs in a positive non-arithmetic literal.
Consider first a rule without any negative literals. To express the rule as an extended relational-algebra view, we write it as a join of all the relations referred to
in the (positive) non-arithmetic literals in the body, followed by a selection. The
selection condition is a conjunction obtained as follows. If p1 (X, Y ), p2 (Y, Z)
occur in the body, where p1 is of the schema (A, B) and p2 is of the schema
(C, D), then p1 .B = p2 .C should belong to the conjunction. The arithmetic
literals can then be added to the condition.
As an example, the Datalog query
query(X, Y) :- works(X, C, S1), works(Y, C, S2), S1 > S2, manages(X, Y)
becomes the following relational-algebra expression:
Exercises
71
E1 = σ(w1.company-name = w2.company-name ∧ w1.salary>w2.salary ∧
manages.person-name = w1.person-name ∧ manages.manager -name = w2.person-name)
(ρw1 (works) × ρw2 (works) × manages)
Now suppose the given rule has negative literals. First suppose that there are
no constants in the negative literals; recall that all variables in a negative literal
must also occur in a positive literal. Let ¬q(X, Y ) be the first negative literal,
and let it be of the schema (E, F ). Let Ei be the relational algebra expression
obtained after all positive and arithmetic literals have been handled. To handle
this negative literal, we generate the expression
Ej
= Ei
1 (ΠA ,A
1
2
(Ei ) − q)
where A1 and A2 are the attribute names of two columns in Ei which correspond to X and Y respectively.
Now let us consider constants occurring in a negative literal. Consider a negative literal of the form ¬q(a, b, Y ) where a and b are constants. Then, in the
above expression defining Ej we replace q by σA1 =a∧A2 =b (q).
Proceeding in a similar fashion, the remaining negative literals are processed,
finally resulting in an expression Ew .
Finally the desired attributes are projected out of the expression. The attributes in Ew corresponding to the variables in the head of the rule become
the projection attributes.
Thus our example rule finally becomes the view:create view query as
Πw1.person-name, w2.person−name (E2 )
If there are multiple rules for the same predicate, the relational-algebra expression defining the view is the union of the expressions corresponding to the
individual rules.
The above conversion can be extended to handle rules that satisfy some weaker
forms of the safety conditions, and where some restricted cases where the variables in arithmetic predicates do not appear in a positive non-arithmetic literal.
C H A P T E R
6
Integrity and Security
This chapter presents several types of integrity constraints, including domain constraints, referential integrity constraints, assertions and triggers, as well as security
and authorization. Referential integrity constraints, and domain constraints are an
important aspect of the specification of a relational database design. Assertions are
seeing increasing use. Triggers are widely used, although each database supports its
own syntax and semantics for triggers; triggers were standardized as part of SQL:1999,
and we can expect databases to provide support for SQL:1999 triggers.
Functional dependencies are now taught as part of normalization instead of being part of the integrity constraints chapter as they were in the 3rd edition. The reason for the change is that they are used almost exclusively in database design, and
no database system to our knowledge supports functional dependencies as integrity
constraints. Covering them in the context of normalization helps motivate students
to spend the effort to understand the intricacies of reasoning with functional dependencies.
Security is a major topic in its own right. Since any system is only as secure as
its weakest component, a system builder must consider all aspects of security. This
chapter focuses only on those security issues that are specific to databases. In an
advanced course, this material can be supplemented by discussion of security issues
in operating systems and in distributed systems.
Changes from 3rd edition:
Trigger coverage is now based on the SQL:1999 standard. At the time of publication of the 3rd edition, triggers had not been standardized. The notion of roles for
authorization has been introduced in this edition, now that it is a part of the SQL:1999
standard. Coverage of encryption has been updated to cover recent developments.
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Chapter 6
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Exercises
6.1 Complete the SQL DDL definition of the bank database of Figure 6.2 to include
the relations loan and borrower.
Answer:
create table loan
(loan-number
char(10),
branch-name char(15),
amount
integer,
primary key (loan-number),
foreign key (branch-name) references branch)
create table borrower
(customer-name char(20),
loan-number
char(10),
primary key (customer-name, loan-number),
foreign key (customer-name) references customer,
foreign key (loan-number) references loan)
Declaring the pair customer-name, loan-number of relation borrower as primary
key ensures that the relation does not contain duplicates.
6.2 Consider the following relational database:
employee (employee-name, street, city)
works (employee-name, company-name, salary)
company (company-name, city)
manages (employee-name, manager-name)
Give an SQL DDL definition of this database. Identify referential-integrity constraints that should hold, and include them in the DDL definition.
Answer:
create table employee
(person-name char(20),
street
char(30),
city
char(30),
primary key (person-name) )
Exercises
75
create table works
(person-name char(20),
company-name char(15),
salary
integer,
primary key (person-name),
foreign key (person-name) references employee,
foreign key (company-name) references company)
create table company
(company-name char(15),
city
char(30),
primary key (company-name))
create table manages
(person-name char(20),
manager-name char(20),
primary key (person-name),
foreign key (person-name) references employee,
foreign key (manager-name) references employee)
Note that alternative datatypes are possible. Other choices for not null attributes may be acceptable.
6.3 Referential-integrity constraints as defined in this chapter involve exactly two
relations. Consider a database that includes the following relations:
salaried-worker (name, office, phone, salary)
hourly-worker (name, hourly-wage)
address (name, street, city)
Suppose that we wish to require that every name that appears in address appear
in either salaried-worker or hourly-worker, but not necessarily in both.
a. Propose a syntax for expressing such constraints.
b. Discuss the actions that the system must take to enforce a constraint of this
form.
Answer:
a. For simplicity, we present a variant of the SQL syntax. As part of the create
table expression for address we include
foreign key (name) references salaried-worker or hourly-worker
b. To enforce this constraint, whenever a tuple is inserted into the address relation, a lookup on the name value must be made on the salaried-worker relation
and (if that lookup failed) on the hourly-worker relation (or vice-versa).
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6.4 SQL allows a foreign-key dependency to refer to the same relation, as in the
following example:
create table manager
(employee-name char(20),
manager-name char(20),
primary key employee-name,
foreign key (manager-name) references manager
on delete cascade )
Here, employee-name is a key to the table manager, meaning that each employee
has at most one manager. The foreign-key clause requires that every manager
also be an employee. Explain exactly what happens when a tuple in the relation
manager is deleted.
Answer: The tuples of all employees of the manager, at all levels, get deleted as
well! This happens in a series of steps. The initial deletion will trigger deletion of
all the tuples corresponding to direct employees of the manager. These deletions
will in turn cause deletions of second level employee tuples, and so on, till all
direct and indirect employee tuples are deleted.
6.5 Suppose there are two relations r and s, such that the foreign key B of r references the primary key A of s. Describe how the trigger mechanism can be used
to implement the on delete cascade option, when a tuple is deleted from s.
Answer: We define triggers for each relation whose primary-key is referred to
by the foreign-key of some other relation. The trigger would be activated whenever a tuple is deleted from the referred-to relation. The action performed by the
trigger would be to visit all the referring relations, and delete all the tuples in
them whose foreign-key attribute value is the same as the primary-key attribute
value of the deleted tuple in the referred-to relation. These set of triggers will
take care of the on delete cascade operation.
6.6 Write an assertion for the bank database to ensure that the assets value for the
Perryridge branch is equal to the sum of all the amounts lent by the Perryridge
branch.
Answer: The assertion-name is arbitrary. We have chosen the name perry. Note
that since the assertion applies only to the Perryridge branch we must restrict
attention to only the Perryridge tuple of the branch relation rather than writing
a constraint on the entire relation.
create assertion perry check
(not exists (select *
from branch
where branch-name = ’Perryridge’ and
assets = (select sum (amount)
from loan
where branch-name = ’Perryridge’)))
Exercises
77
6.7 Write an SQL trigger to carry out the following action: On delete of an account,
for each owner of the account, check if the owner has any remaining accounts,
and if she does not, delete her from the depositor relation.
Answer:
create trigger check-delete-trigger after delete on account
referencing old row as orow
for each row
delete from depositor
where depositor.customer-name not in
( select customer-name from depositor
where account-number <> orow.account-number )
end
6.8 Consider a view branch-cust defined as follows:
create view branch-cust as
select branch-name, customer-name
from depositor, account
where depositor.account-number = account.account-number
Suppose that the view is materialized, that is, the view is computed and stored.
Write active rules to maintain the view, that is, to keep it up to date on insertions
to and deletions from depositor or account. Do not bother about updates.
Answer: For inserting into the materialized view branch-cust we must set a
database trigger on an insert into depositor and account. We assume that the
database system uses immediate binding for rule execution. Further, assume that
the current version of a relation is denoted by the relation name itself, while the
set of newly inserted tuples is denoted by qualifying the relation name with the
prefix – inserted.
The active rules for this insertion are given below –
define trigger insert into branch-cust via depositor
after insert on depositor
referencing new table as inserted for each statement
insert into branch-cust
select branch-name, customer-name
from inserted, account
where inserted.account-number = account.account-number
define trigger insert into branch-cust via account
after insert on account
referencing new table as inserted for each statement
insert into branch-cust
select branch-name, customer-name
from depositor, inserted
where depositor.account-number = inserted.account-number
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Chapter 6
Integrity and Security
Note that if the execution binding was deferred (instead of immediate), then
the result of the join of the set of new tuples of account with the set of new tuples
of depositor would have been inserted by both active rules, leading to duplication
of the corresponding tuples in branch-cust.
The deletion of a tuple from branch-cust is similar to insertion, except that
a deletion from either depositor or account will cause the natural join of these
relations to have a lesser number of tuples. We denote the newly deleted set of
tuples by qualifying the relation name with the keyword deleted.
define trigger delete from branch-cust via depositor
after delete on depositor
referencing old table as deleted for each statement
delete from branch-cust
select branch-name, customer-name
from deleted, account
where deleted.account-number = account.account-number
define trigger delete from branch-cust via account
after delete on account
referencing old table as deleted for each statement
delete from branch-cust
select branch-name, customer-name
from depositor, deleted
where depositor.account-number = deleted.account-number
6.9 Make a list of security concerns for a bank. For each item on your list, state
whether this concern relates to physical security, human security, operatingsystem security, or database security.
Answer: Let us consider the problem of protecting our sample bank database.
Some security measures at each of the four levels are mentioned below a. Physical level - The system from which the relations can be accessed and
modified should be placed in a locked, well-guarded, and impregnable room.
b. Human level - A proper key transfer policy should be enforced for restricting access to the “system room” mentioned above. Passwords for gaining
access to the database should be known only to trusted users.
c. Operating System level - Login passwords should be difficult to guess and
they should be changed regularly. No user should be able to gain unauthorized access to the system due to a software bug in the operating system.
d. Database System level - The users should be authorized access only to relevant parts of the database. For example, a bank teller should be allowed to
modify values for the customer’s balance, but not for her own salary.
6.10 Using the relations of our sample bank database, write an SQL expression to
define the following views:
a. A view containing the account numbers and customer names (but not the
balances) for all accounts at the Deer Park branch.
Exercises
79
b. A view containing the names and addresses of all customers who have an
account with the bank, but do not have a loan.
c. A view containing the name and average account balance of every customer
of the Rock Ridge branch.
Answer:
a.
create view deer-park as
select account-number, customer-name
from depositor, account
where branch-name = ’Deer Park’ and
depositor.account-number = account.account-number
b.
create view no-debt as
select * from customer
where customer-name in
(select customer-name
from depositor)
minus
(select customer-name
from borrower)
c.
create view avg-bal as
select customer-name, avg(balance)
from depositor, account
where depositor.account-number = account.account-number
and branch-name = ’Rock Ridge’
group by customer-name
6.11 For each of the views that you defined in Exercise 6.10, explain how updates
would be performed (if they should be allowed at all). Hint: See the discussion
of views in Chapter 3.
Answer: To insert (account-number, name) into the view deer-park we insert the
tuple (Deer Park, account-number, null) into the account relation and the tuple
(name, account-number) into the depositor relation.
Updates to the views no-debt and avg-bal present serious problems. If we insert
into the no-debt view, the system must reject the insertion if the customer has a
loan. The overhead of updating through this view is so high that most systems
would disallow update. The avg-bal view cannot be updated since the result of
an aggregate operation depends on several tuples, not just one.
6.12 In Chapter 3, we described the use of views to simplify access to the database
by users who need to see only part of the database. In this chapter, we described
the use of views as a security mechanism. Do these two purposes for views ever
conflict? Explain your answer.
Answer: Usually, a well-designed view and security mechanism can avoid con-
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Chapter 6
Integrity and Security
flicts between ease of access and security. However, as the following example
shows, the two purposes do conflict in case the mechanisms are not designed
carefully.
Suppose we have a database of employee data and a user whose view involves employee data for employees earning less than $10,000. If this user inserts employee Jones, whose salary is $9,000, but accidentally enters $90,000,
several existing database systems will accept this update as a valid update through
a view. However, the user will be denied access to delete this erroneous tuple
by the security mechanism.
6.13 What is the purpose of having separate categories for index authorization and
resource authorization?
Answer: Index and resource authorization should be special categories to allow certain users to create relations (and the indices to operate on them) while
preventing these time-consuming and schema-changing operations from being
available to many users. Separating index and resource authorization allows a
user to build an index on existing relations, say, for optimization purposes, but
allows us to deny that user the right to create new relations.
6.14 Database systems that store each relation in a separate operating-system file
may use the operating system’s security and authorization scheme, instead of
defining a special scheme themselves. Discuss an advantage and a disadvantage
of such an approach.
Answer: Database systems have special requirements which are typically more
refined than most operating systems. For example, a single user may have different privileges on different files throughout the system, including changing
indices and attributes which file systems typically don’t monitor. The advantage of using the operating system’s security mechanism is that it simplifies the
database system and can be used for simple (read/write) security measures.
6.15 What are two advantages of encrypting data stored in the database?
Answer:
a. Encrypted data allows authorized users to access data without worrying
about other users or the system administrator gaining any information.
b. Encryption of data may simplify or even strengthen other authorization
mechanisms. For example, distribution of the cryptographic key amongst
only trusted users is both, a simple way to control read access, and an added
layer of security above that offered by views.
6.16 Perhaps the most important data items in any database system are the passwords that control access to the database. Suggest a scheme for the secure storage of passwords. Be sure that your scheme allows the system to test passwords
supplied by users who are attempting to log into the system.
Answer: A scheme for storing passwords would be to encrypt each password,
and then use a hash index on the user-id. The user-id can be used to easily access
the encrypted password. The password being used in a login attempt is then encrypted and compared with the stored encryption of the correct password. An
Exercises
81
advantage of this scheme is that passwords are not stored in clear text and the
code for decryption need not even exist!
C H A P T E R
7
Relational-Database Design
This chapter presents the principles of relational database design. Undergraduates
frequently find this chapter difficult. It is acceptable to cover only Sections 7.1, 7.2
and 7.4 for classes that find the material particularly difficult. However, a careful
study of data dependencies and normalization is a good way to introduce students
to the formal aspects of relational database theory.
There are many ways of stating the definitions of the normal forms. We have chosen a style which we think is the easiest to present and which most clearly conveys
the intuition of the normal forms.
Changes from 3rd edition:
There are many changes to this chapter from the 3rd edition. 1NF is now defined
formally. Functional dependencies are now covered in this chapter, instead of Chapter 6. The reason is that normalization provides the real motivation for functional
dependencies, since they are used primarily for normalization.
We have described a simplified procedure for functional dependency inference
based on attribute closure, and provided simplified procedures to test for normal
forms.
Coverage of multivalued dependency theory and normal forms beyond 4NF (that
is, PJNF and DKNF) has been moved into Appendix C (which is available on the
web, not in the print form of the book).
The process of practical relational schema design has been described in significantly more detail, along with some design problems that are not caught by the usual
normalization process.
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Chapter 7
Relational-Database Design
Exercises
7.1 Explain what is meant by repetition of information and inability to represent information. Explain why each of these properties may indicate a bad relationaldatabase design.
Answer:
• Repetition of information is a condition in a relational database where the
values of one attribute are determined by the values of another attribute
in the same relation, and both values are repeated throughout the relation.
This is a bad relational database design because it increases the storage required for the relation and it makes updating the relation more difficult.
• Inability to represent information is a condition where a relationship exists
among only a proper subset of the attributes in a relation. This is bad relational database design because all the unrelated attributes must be filled
with null values otherwise a tuple without the unrelated information cannot be inserted into the relation.
• Loss of information is a condition of a relational database which results from
the decomposition of one relation into two relations and which cannot be
combined to recreate the original relation. It is a bad relational database
design because certain queries cannot be answered using the reconstructed
relation that could have been answered using the original relation.
7.2 Suppose that we decompose the schema R = (A, B, C, D, E) into
(A, B, C)
(A, D, E).
Show that this decomposition is a lossless-join decomposition if the following
set F of functional dependencies holds:
A → BC
CD → E
B→D
E→A
Answer: A decomposition {R1 , R2 } is a lossless-join decomposition if R1 ∩
R2 → R1 or R1 ∩ R2 → R2 . Let R1 = (A, B, C), R2 = (A, D, E), and R1 ∩
R2 = A. Since A is a candidate key (see Exercise 7.11), Therefore R1 ∩ R2 →
R1 .
7.3 Why are certain functional dependencies called trivial functional dependencies?
Answer: Certain functional dependencies are called trivial functional dependencies because they are satisfied by all relations.
7.4 List all functional dependencies satisfied by the relation of Figure 7.21.
Answer: The nontrivial functional dependencies are: A → B and C → B,
Exercises
85
and a dependency they logically imply: AC → B. There are 19 trivial functional dependencies of the form α → β, where β ⊆ α. C does not functionally
determine A because the first and third tuples have the same C but different A
values. The same tuples also show B does not functionally determine A. Likewise, A does not functionally determine C because the first two tuples have the
same A value and different C values. The same tuples also show B does not
functionally determine C.
7.5 Use the definition of functional dependency to argue that each of Armstrong’s
axioms (reflexivity, augmentation, and transitivity) is sound.
Answer: The definition of functional dependency is: α → β holds on R if in any
legal relation r(R), for all pairs of tuples t1 and t2 in r such that t1 [α] = t2 [α], it
is also the case that t1 [β] = t2 [β].
Reflexivity rule: if α is a set of attributes, and β ⊆ α, then α → β.
Assume ∃ t1 and t2 such that t1 [α] = t2 [α]
t1 [β] = t2 [β] since β ⊆ α
α → β
definition of FD
Augmentation rule: if α → β, and γ is a set of attributes, then γ α → γ β.
Assume ∃ t1 , t2 such that t1 [γ α] = t2 [γ α]
γ ⊆ γα
t1 [γ] = t2 [γ]
t1 [α] = t2 [α]
α ⊆ γα
t1 [β] = t2 [β]
definition of α → β
t1 [γ β] = t2 [γ β] γ β = γ ∪ β
γα → γβ
definition of FD
Transitivity rule: if α → β and β → γ, then α → γ.
Assume ∃ t1 , t2 such that t1 [α] = t2 [α]
t1 [β] = t2 [β]
t1 [γ] = t2 [γ]
α → γ
definition of α → β
definition of β → γ
definition of FD
7.6 Explain how functional dependencies can be used to indicate the following:
• A one-to-one relationship set exists between entity sets account and customer.
• A many-to-one relationship set exists between entity sets account and customer.
A
a1
a1
a2
a2
B
b1
b1
b1
b1
C
c1
c2
c1
c3
Figure 7.21. Relation of Exercise 7.4.
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Chapter 7
Relational-Database Design
Answer: Let P k(r) denote the primary key attribute of relation r.
• The functional dependencies P k(account) → P k (customer) and P k(customer)
→ P k(account) indicate a one-to-one relationship because any two tuples
with the same value for account must have the same value for customer,
and any two tuples agreeing on customer must have the same value for
account.
• The functional dependency P k(account) → P k(customer) indicates a manyto-one relationship since any account value which is repeated will have the
same customer value, but many account values may have the same customer value.
7.7 Consider the following proposed rule for functional dependencies: If α → β and
γ → β, then α → γ. Prove that this rule is not sound by showing a relation r that
satisfies α → β and γ → β, but does not satisfy α → γ.
Answer: Consider the following rule: if A → B and C → B, then A → C.
That is, α = A, β = B, γ = C. The following relation r is a counterexample
to the rule.
r: A B C
a 1 b 1 c1
a 1 b 1 c2
Note: A → B and C → B, (since no 2 tuples have the same C value,
C → B is true trivially). However, it is not the case that A → C since the same
A value is in two tuples, but the C value in those tuples disagree.
7.8 Use Armstrong’s axioms to prove the soundness of the union rule. (Hint: Use the
augmentation rule to show that, if α → β, then α → αβ. Apply the augmentation
rule again, using α → γ, and then apply the transitivity rule.)
Answer: To prove that:
if α → β and α → γ then α → βγ
Following the hint, we derive:
α → β
given
αα → αβ augmentation rule
α → αβ
union of identical sets
α → γ
given
αβ → γ β augmentation rule
α → βγ
transitivity rule and set union commutativity
7.9 Use Armstrong’s axioms to prove the soundness of the decomposition rule.
Answer: The decomposition rule, and its derivation from Armstrong’s axioms
are given below:
Exercises
87
if α → βγ, then α → β and α → γ.
α → βγ
βγ → β
α → β
βγ → γ
α → γ
given
reflexivity rule
transitivity rule
reflexive rule
transitive rule
7.10 Use Armstrong’s axioms to prove the soundness of the pseudotransitivity rule.
Answer: Proof using Armstrong’s axioms of the Pseudotransitivity Rule:
if α → β and γ β → δ, then αγ → δ.
α → β
αγ → γ β
γβ → δ
αγ → δ
given
augmentation rule and set union commutativity
given
transitivity rule
7.11 Compute the closure of the following set F of functional dependencies for relation schema R = (A, B, C, D, E).
A → BC
CD → E
B→D
E→A
List the candidate keys for R.
Answer: Compute the closure of the following set F of functional dependencies
for relation schema R = (A, B, C, D, E).
A → BC
CD → E
B→D
E→A
List the candidate keys for R.
Note: It is not reasonable to expect students to enumerate all of F + . Some shorthand representation of the result should be acceptable as long as the nontrivial
members of F + are found.
Starting with A → BC, we can conclude: A → B and A → C.
Since A → B and B → D, A → D
Since A → CD and CD → E, A → E
Since A → A, we have
A → ABCDE from the above steps
Since E → A, E → ABCDE
Since CD → E, CD → ABCDE
Since B → D and BC → CD, BC → ABCDE
Also, C → C, D → D, BD → D, etc.
(decomposition, transitive)
(union, decomposition, transitive)
(reflexive)
(union)
(transitive)
(transitive)
(augmentative, transitive)
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Relational-Database Design
Therefore, any functional dependency with A, E, BC, or CD on the left hand
side of the arrow is in F + , no matter which other attributes appear in the FD.
Allow * to represent any set of attributes in R, then F + is BD → B, BD → D,
C → C, D → D, BD → BD, B → D, B → B, B → BD, and all FDs of
the form A ∗ → α, BC ∗ → α, CD ∗ → α, E ∗ → α where α is any subset of
{A, B, C, D, E}. The candidate keys are A, BC, CD, and E.
7.12 Using the functional dependencies of Exercise 7.11, compute B + .
Answer: Computing B + by the algorithm in Figure 7.7 we start with result =
{B}. Considering FDs of the form β → γ in F , we find that the only dependencies satisfying β ⊆ result are B → B and B → D. Therefore result =
{B, D}. No more dependencies in F apply now. Therefore B + = {B, D}
7.13 Using the functional dependencies of Exercise 7.11, compute the canonical
cover Fc .
Answer: The given set of FDs F is:A → BC
CD → E
B→D
E→A
The left side of each FD in F is unique. Also none of the attributes in the left
side or right side of any of the FDs is extraneous. Therefore the canonical cover
Fc is equal to F .
7.14 Consider the algorithm in Figure 7.22 to compute α+ . Show that this algorithm
is more efficient than the one presented in Figure 7.7 (Section 7.3.3) and that it
computes α+ correctly.
Answer: The algorithm is correct because:
• If A is added to result then there is a proof that α → A. To see this, observe
that α → α trivially so α is correctly part of result. If A ∈ α is added to
result there must be some FD β → γ such that A ∈ γ and β is already a
subset of result. (Otherwise f dcount would be nonzero and the if condition
would be false.) A full proof can be given by induction on the depth of
recursion for an execution of addin, but such a proof can be expected only
from students with a good mathematical background.
• If A ∈ α+ , then A is eventually added to result. We prove this by induction
on the length of the proof of α → A using Armstrong’s axioms. First observe
that if procedure addin is called with some argument β, all the attributes in
β will be added to result. Also if a particular FD’s fdcount becomes 0, all
the attributes in its tail will definitely be added to result. The base case of
the proof, A ∈ α ⇒ A ∈ α+ , is obviously true because the first call to
addin has the argument α. The inductive hypotheses is that if α → A can
be proved in n steps or less then A ∈ result. If there is a proof in n + 1
Exercises
result := ∅;
/* fdcount is an array whose ith element contains the number
of attributes on the left side of the ith FD that are
not yet known to be in α+ */
for i := 1 to |F | do
begin
let β → γ denote the ith FD;
fdcount [i] := |β|;
end
/* appears is an array with one entry for each attribute. The
entry for attribute A is a list of integers. Each integer
i on the list indicates that A appears on the left side
of the ith FD */
for each attribute A do
begin
appears [A] := N IL;
for i := 1 to |F | do
begin
let β → γ denote the ith FD;
if A ∈ β then add i to appears [A];
end
end
addin (α);
return (result);
procedure addin (α);
for each attribute A in α do
begin
if A ∈ result then
begin
result := result ∪ {A};
for each element i of appears[A] do
begin
fdcount [i] := fdcount [i] − 1;
if fdcount [i] := 0 then
begin
let β → γ denote the ith FD;
addin (γ);
end
end
end
end
Figure 7.22. An algorithm to compute α+ .
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steps that α → A, then the last step was an application of either reflexivity,
augmentation or transitivity on a fact α → β proved in n or fewer steps.
If reflexivity or augmentation was used in the (n + 1)st step, A must have
been in result by the end of the nth step itself. Otherwise, by the inductive
hypothesis β ⊆ result. Therefore the dependency used in proving β → γ,
A ∈ γ will have f dcount set to 0 by the end of the nth step. Hence A will
be added to result.
To see that this algorithm is more efficient than the one presented in the chapter note that we scan each FD once in the main program. The resulting array
appears has size proportional to the size of the given FDs. The recursive calls to
addin result in processing linear in the size of appears. Hence the algorithm has
time complexity which is linear in the size of the given FDs. On the other hand,
the algorithm given in the text has quadratic time complexity, as it may perform
the loop as many times as the number of FDs, in each loop scanning all of them
once.
7.15 Given the database schema R(a, b, c), and a relation r on the schema R, write an
SQL query to test whether the functional dependency b → c holds on relation
r. Also write an SQL assertion that enforces the functional dependency. Assume
that no null values are present.
Answer:
a. The query is given below. Its result is non-empty if and only if b → c does
not hold on r.
select b
from r
group by b
having count(distinct c) > 1
b.
create assertion b-to-c check
(not exists
(select b
from r
group by b
having count(distinct c) > 1
)
)
7.16 Show that the following decomposition of the schema R of Exercise 7.2 is not a
lossless-join decomposition:
(A, B, C)
(C, D, E).
Exercises
91
Hint: Give an example of a relation r on schema R such that
1
ΠA, B, C (r)
ΠC, D, E (r) = r
Answer: Following the hint, use the following example of r:
A B
a1 b 1
a2 b 2
With R1
C D E
c1 d1 e1
c1 d2 e2
= (A, B, C), R2 = (C, D, E) :
a. ΠR1 (r) would be:
A
a1
a2
B
b1
b2
C
c1
c1
b. ΠR2 (r) would be:
C
c1
c1
c. ΠR1 (r)
A
a1
a1
a2
a2
D
d1
d2
1
B
b1
b1
b2
b2
E
e1
e2
ΠR2 (r) would be:
C
c1
c1
c1
c1
Clearly, ΠR1 (r)
D
d1
d2
d1
d2
1
E
e1
e2
e1
e2
ΠR2 (r) = r. Therefore, this is a lossy join.
7.17 Let R1 , R2 , . . . , Rn be a decomposition of schema U. Let u(U ) be a relation, and
let ri = ΠRI (u). Show that
u ⊆ r1
1
r2
1
···
1
rn
Answer: Consider some tuple t in u.
Note that ri = ΠRi (u) implies that t[Ri ] ∈ ri , 1 ≤ i ≤ n. Thus,
t[R1 ]
1
t[R2 ]
1
...
1
t[Rn ] ∈ r1
1
r2
1
...
1
rn
By the definition of natural join,
t[R1 ]
1
t[R2 ]
1
...
1
t[Rn ] = Πα (σβ (t[R1 ] × t[R2 ] × . . . × t[Rn ]))
where the condition β is satisfied if values of attributes with the same name
in a tuple are equal and where α = U . The cartesian product of single tuples
generates one tuple. The selection process is satisfied because all attributes with
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the same name must have the same value since they are projections from the
same tuple. Finally, the projection clause removes duplicate attribute names.
By the definition of decomposition, U = R1 ∪ R2 ∪ . . . ∪ Rn , which means that
all attributes of t are in t[R1 ] 1 t[R2 ] 1 . . . 1 t[Rn ]. That is, t is equal to the result
of this join.
Since t is any arbitrary tuple in u,
u ⊆ r1
1
r2
1
...
1
rn
7.18 Show that the decomposition in Exercise 7.2 is not a dependency-preserving
decomposition.
Answer: The dependency B → D is not preserved. F1 , the restriction of F to
(A, B, C) is A → ABC, A → AB, A → AC, A → BC, A → B, A → C,
A → A, B → B, C → C, AB → AC, AB → ABC, AB → BC, AB → AB,
AB → A, AB → B, AB → C, AC (same as AB), BC (same as AB), ABC
(same as AB). F2 , the restriction of F to (C, D, E) is A → ADE, A → AD,
A → AE, A → DE, A → A, A → D, A → E, D → D, E (same as A), AD,
AE, DE, ADE (same as A). (F1 ∪ F2 )+ is easily seen not to contain B → D
since the only FD in F1 ∪ F2 with B as the left side is B → B, a trivial FD. We
shall see in Exercise 7.22 that B → D is indeed in F + . Thus B → D is not
preserved. Note that CD → ABCDE is also not preserved.
A simpler argument is as follows: F1 contains no dependencies with D on the
right side of the arrow. F2 contains no dependencies with B on the left side of
the arrow. Therefore for B → D to be preserved there must be an FD B → α
in F1+ and α → D in F2+ (so B → D would follow by transitivity). Since the
intersection of the two schemes is A, α = A. Observe that B → A is not in F1+
since B + = BD.
7.19 Show that it is possible to ensure that a dependency-preserving decomposition into 3NF is a lossless-join decomposition by guaranteeing that at least one
schema contains a candidate key for the schema being decomposed. (Hint: Show
that the join of all the projections onto the schemas of the decomposition cannot
have more tuples than the original relation.)
Answer: Let F be a set of functional dependencies that hold on a schema R. Let
σ = {R1 , R2 , . . . , Rn } be a dependency-preserving 3NF decomposition of R. Let
X be a candidate key for R.
Consider a legal instance r of R. Let j = ΠX (r) 1 ΠR1 (r) 1 ΠR2 (r) . . . 1
ΠRn (r). We want to prove that r = j.
We claim that if t1 and t2 are two tuples in j such that t1 [X] = t2 [X], then
t1 = t2 . To prove this claim, we use the following inductive argument –
Let F = F1 ∪ F2 ∪ . . . ∪ Fn , where each Fi is the restriction of F to the schema
Ri in σ. Consider the use of the algorithm given in Figure 7.7 to compute the
closure of X under F . We use induction on the number of times that the f or
loop in this algorithm is executed.
• Basis : In the first step of the algorithm, result is assigned to X, and hence
given that t1 [X] = t2 [X], we know that t1 [result] = t2 [result] is true.
Exercises
93
• Induction Step : Let t1 [result] = t2 [result] be true at the end of the k th execution of the f or loop.
Suppose the functional dependency considered in the k + 1 th execution
of the f or loop is β → γ, and that β ⊆ result. β ⊆ result implies that
t1 [β] = t2 [β] is true. The facts that β → γ holds for some attribute set Ri
in σ, and that t1 [Ri ] and t2 [Ri ] are in ΠRi (r) imply that t1 [γ] = t2 [γ] is
also true. Since γ is now added to result by the algorithm, we know that
t1 [result] = t2 [result] is true at the end of the k + 1 th execution of the f or
loop.
Since σ is dependency-preserving and X is a key for R, all attributes in R are in
result when the algorithm terminates. Thus, t1 [R] = t2 [R] is true, that is, t1 = t2
– as claimed earlier.
Our claim implies that the size of ΠX (j) is equal to the size of j. Note also
that ΠX (j) = ΠX (r) = r (since X is a key for R). Thus we have proved that the
size of j equals that of r. Using the result of Exercise 7.17, we know that r ⊆ j.
Hence we conclude that r = j.
Note that since X is trivially in 3NF, σ ∪ {X} is a dependency-preserving
lossless-join decomposition into 3NF.
7.20 List the three design goals for relational databases, and explain why each is desirable.
Answer: The three design goals are lossless-join decompositions, dependency
preserving decompositions, and minimization of repetition of information. They
are desirable so we can maintain an accurate database, check correctness of updates quickly, and use the smallest amount of space possible.
7.21 Give a lossless-join decomposition into BCNF of schema R of Exercise 7.2.
Answer: From Exercise 7.11, we know that B → D is nontrivial and the left
hand side is not a superkey. By the algorithm of Figure 7.13 we derive the relations {(A, B, C, E), (B, D)}. This is in BCNF.
7.22 Give an example of a relation schema R and set F of functional dependencies
such that there are at least three distinct lossless-join decompositions of R into
BCNF.
Answer: Given the relation R = (A, B, C, D) the set of functional dependencies F = A → B, C → D, B → C allows three distinct BCNF decompositions.
R1 = {(A, B), (C, D), (B, C)}
is in BCNF as is
R2 = {(A, B), (C, D), (A, C)}
R2 = {(A, B), (C, D), (A, C)}
R3 = {(B, C), (A, D), (A, B)}
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7.23 In designing a relational database, why might we choose a non-BCNF design?
Answer: BCNF is not always dependency preserving. Therefore, we may want
to choose another normal form (specifically, 3NF) in order to make checking dependencies easier during updates. This would avoid joins to check dependencies and increase system performance.
7.24 Give a lossless-join, dependency-preserving decomposition into 3NF of schema
R of Exercise 7.2.
Answer: First we note that the dependencies given in Exercise 7.2 form a canonical cover. Generating the schema from the algorithm of Figure 7.14 we get
R = {(A, B, C), (C, D, E), (B, D), (E, A)}.
Schema (A, B, C) contains a candidate key. Therefore R is a third normal form
dependency-preserving lossless-join decomposition.
Note that the original schema R = (A, B, C, D, E) is already in 3NF. Thus,
it was not necessary to apply the algorithm as we have done above. The single
original schema is trivially a lossless join, dependency-preserving decomposition.
7.25 Let a prime attribute be one that appears in at least one candidate key. Let α and
β be sets of attributes such that α → β holds, but β → α does not hold. Let A be
an attribute that is not in α, is not in β, and for which β → A holds. We say that
A is transitively dependent on α. We can restate our definition of 3NF as follows:
A relation schema R is in 3NF with respect to a set F of functional dependencies
if there are no nonprime attributes A in R for which A is transitively dependent
on a key for R.
Show that this new definition is equivalent to the original one.
Answer: Suppose R is in 3NF according to the textbook definition. We show
that it is in 3NF according to the definition in the exercise. Let A be a nonprime
attribute in R that is transitively dependent on a key α for R. Then there exists
β ⊆ R such that β → A, α → β, A ∈ α, A ∈ β, and β → α does not hold.
But then β → A violates the textbook definition of 3NF since
• A ∈ β implies β → A is nontrivial
• Since β → α does not hold, β is not a superkey
• A is not any candidate key, since A is nonprime
Now we show that if R is in 3NF according to the exercise definition, it is in 3NF
according to the textbook definition. Suppose R is not in 3NF according the the
textbook definition. Then there is an FD α → β that fails all three conditions.
Thus
• α → β is nontrivial.
• α is not a superkey for R.
• Some A in β − α is not in any candidate key.
This implies that A is nonprime and α → A. Let γ be a candidate key for R.
Then γ → α, α → γ does not hold (since α is not a superkey), A ∈ α, and
Exercises
95
A ∈ γ (since A is nonprime). Thus A is transitively dependent on γ, violating
the exercise definition.
7.26 A functional dependency α → β is called a partial dependency if there is a
proper subset γ of α such that γ → β. We say that β is partially dependent on α. A
relation schema R is in second normal form (2NF) if each attribute A in R meets
one of the following criteria:
• It appears in a candidate key.
• It is not partially dependent on a candidate key.
Show that every 3NF schema is in 2NF. (Hint: Show that every partial dependency is a transitive dependency.)
Answer: Referring to the definitions in Exercise 7.25, a relation schema R is said
to be in 3NF if there is no non-prime attribute A in R for which A is transitively
dependent on a key for R.
We can also rewrite the definition of 2NF given here as :
“A relation schema R is in 2NF if no non-prime attribute A is partially dependent
on any candidate key for R.”
To prove that every 3NF schema is in 2NF, it suffices to show that if a nonprime attribute A is partially dependent on a candidate key α, then A is also
transitively dependent on the key α.
Let A be a non-prime attribute in R. Let α be a candidate key for R. Suppose
A is partially dependent on α.
• From the definition of a partial dependency, we know that for some proper
subset β of α, β → A.
• Since β ⊂ α, α → β. Also, β → α does not hold, since α is a candidate key.
• Finally, since A is non-prime, it cannot be in either β or α.
Thus we conclude that α → A is a transitive dependency. Hence we have proved
that every 3NF schema is also in 2NF.
7.27 Given the three goals of relational-database design, is there any reason to design
a database schema that is in 2NF, but is in no higher-order normal form? (See
Exercise 7.26 for the definition of 2NF.)
Answer: The three design goals of relational databases are to avoid
• Repetition of information
• Inability to represent information
• Loss of information.
2NF does not prohibit as much repetition of information since the schema (A, B, C)
with dependencies A → B and B → C is allowed under 2NF, although the
same (B, C) pair could be associated with many A values, needlessly duplicating C values. To avoid this we must go to 3NF. Repetition of information is
allowed in 3NF in some but not all of the cases where it is allowed in 2NF. Thus,
in general, 3NF reduces repetition of information. Since we can always achieve a
lossless join 3NF decomposition, there is no loss of information needed in going
from 2NF to 3NF.
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Note that the decomposition {(A, B), (B, C)} is a dependency-preserving
and lossless-loin 3NF decomposition of the schema (A, B, C). However, in case
we choose this decomposition, retrieving information about the relationship between A, B and C requires a join of two relations, which is avoided in the corresponding 2NF decomposition.
Thus, the decision of which normal form to choose depends upon how the
cost of dependency checking compares with the cost of the joins. Usually, the
3NF would be preferred. Dependency checks need to be made with every insert
or update to the instances of a 2NF schema, whereas, only some queries will
require the join of instances of a 3NF schema.
7.28 Give an example of a relation schema R and a set of dependencies such that R is
in BCNF, but is not in 4NF.
Answer: The relation schema R = (A, B, C, D, E) and the set of dependencies
A →
→ BC
B →
→ CD
E →
→ AD
constitute a BCNF decomposition, however it is clearly not in 4NF. (It is BCNF
because all FDs are trivial).
7.29 Explain why 4NF is a normal form more desirable than BCNF.
Answer: 4NF is more desirable than BCNF because it reduces the repetition of
information. If we consider a BCNF schema not in 4NF (see Exercise 7.28), we
observe that decomposition into 4NF does not lose information provided that a
lossless join decomposition is used, yet redundancy is reduced.
7.30 Explain how dangling tuples may arise. Explain problems that they may cause.
Answer: Dangling tuples can arise when one tuple is inserted into a decomposed relation but no corresponding tuple is inserted into the other relations in
the decomposition. They can cause incorrect values to be returned by queries
which form the join of a decomposed relation since the dangling tuple might
not be included. As we saw in Chapter 5, dangling tuples can be avoided by the
specification of referential integrity constraints.
C H A P T E R
8
Object-Oriented Databases
This chapter provides an introduction to object-oriented databases. This chapter and
the next chapter form a logical unit and should be taught consecutively. It is possible
to teach these chapters before covering normalization (Chapter 7).
The sections of the chapter prior to the section on persistent C++ and ODMG (Section 8.5) do not assume any familiarity with an object-oriented programming language. However, it is quite possible that students may already be familiar with the
basic concepts of object orientation, and with an object-oriented programming languages. For such students Section 8.2 can be covered relatively quickly. However, it
is important to point out the motivation for object-oriented features in the context of
a database, and how the requirements differ from those of a programming language.
There is a tendency to confuse “persistent” object-oriented languages with objectoriented databases. A persistent object-oriented language should be merely a frontend to a database. It is important to remind students of all of the features that a
database system must have, so that, they can distinguish full-fledged object-oriented
database systems from systems that provide an object-oriented front-end, but provide little in the way of database facilities such as a query facility, an on-line catalog,
concurrency control and recovery.
There are several commercial object-oriented database systems available on the
market, and a few public domain systems as well. Some of the commercial systems
also offer low-cost or free copies for academic use. The commercial object-oriented
database systems include Objectivity (www.objectivity.com), ObjectStore (www.odi.com),
and Versant (www.versant.com).
Changes from 3rd edition:
Some examples have been updated to make them more intuitive. The coverage of
ODMG has been updated to ODMG-2, including the new syntax (with a d prefix for
keywords), and the new d rel ref feature to declare relationships.
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Exercises
8.1 For each of the following application areas, explain why a relational database
system would be inadequate. List all specific system components that would
need to be modified.
a. Computer-aided design
b. Multimedia databases
Answer: Each of the applications includes large, specialized data items (e.g.,
a program module, a graphic image, digitized voice, a document). These data
items have operations specific to them (e.g., compile, rotate, play, format) that
cannot be expressed in relational query languages. These data items are of variable length making it impractical to store them in the short fields that are allowed in records for such database systems. Thus, the data model, data manipulation language, and data definition language need to be changed.
Also, long-duration and nested transactions are typical of these applications.
Changes to the concurrency and recovery subsystems are likely to be needed.
8.2 How does the concept of an object in the object-oriented model differ from the
concept of an entity in the entity-relationship model?
Answer: An entity is simply a collection of variables or data items. An object is
an encapsulation of data as well as the methods (code) to operate on the data.
The data members of an object are directly visible only to its methods. The outside world can gain access to the object’s data only by passing pre-defined messages to it, and these messages are implemented by the methods.
8.3 A car-rental company maintains a vehicle database for all vehicles in its current
fleet. For all vehicles, it includes the vehicle identification number, license number, manufacturer, model, date of purchase, and color. Special data are included
for certain types of vehicles:
• Trucks: cargo capacity
• Sports cars: horsepower, renter age requirement
• Vans: number of passengers
• Off-road vehicles: ground clearance, drivetrain (four- or two-wheel drive)
Construct an object-oriented database schema definition for this database. Use
inheritance where appropriate.
Answer:
class vehicle {
int
string
string
string
date
vehicle-id;
license-number;
manufacturer;
model;
purchase-date;
Exercises
};
color-type
99
color;
class truck isa vehicle {
int
cargo-capacity;
};
class sports-car isa vehicle {
int
horsepower;
int
renter-age-requirement;
};
class van isa vehicle {
int
num-passengers;
};
class off-road-vehicle isa vehicle {
real
ground-clearance;
drivetrain-type drivetrain;
};
We assume that color-type and drivetrain-type are previously defined types.
8.4 Explain why ambiguity potentially exists with multiple inheritance. Illustrate
your explanation with an example.
Answer: A class inherits the variables and methods of all its immediate superclasses. Thus it could inherit a variable or method of the same name from more
than one super-class. When that particular variable or method of an object of
the sub-class is referenced, there is an ambiguity regarding which of the superclasses provides the inheritance.
For instance, let there be classes teacher and student, both having a variable
department. If a class teachingAssistant inherits from both of these classes, any
reference to the department variable of a teachingAssistant object is ambiguous.
8.5 Explain how the concept of object identity in the object-oriented model differs
from the concept of tuple equality in the relational model.
Answer: Tuple equality is determined by data values. Object identity is independent of data values, since object-oriented systems use built-in identity.
8.6 Explain the distinction in meaning between edges in a DAG representing inheritance and a DAG representing object containment.
Answer: An edge from class A to class B in the DAG representing inheritance
means that an object of class B is also an object of class A. It has all the properties
that objects of class A have, plus additional ones of its own. In particular, it
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inherits all the variables and methods of class A. It can of course provide its
own implementations for the inherited methods.
And edge from class A to class B in the object containment DAG means that
an object of class A contains an object of class B. There need not be any similarities in the properties of A and B. Neither B nor A inherit anything from the
other. They function as independent types, to the extent that an object of class
A can access the variables of the B object contained in it only via the B object’s
methods.
8.7 Why do persistent programming languages allow transient objects? Might it be
simpler to use only persistent objects, with unneeded objects deleted at the end
of an execution? Explain your answer.
Answer: Creation, destruction and access will typically be more time consuming and expensive for persistent objects stored in the database, than for transient objects in the transaction’s local memory. This is because of the over-heads
in preserving transaction semantics, security and integrity. Since a transient object is purely local to the transaction which created it and does not enter the
database, all these over-heads are avoided. Thus, in order to provide efficient
access to purely local and temporary data, transient objects are provided by
persistent programming languages.
8.8 Using ODMG C++
a. Give schema definitions corresponding to the relational schema shown in
Figure 3.39, using references to express foreign-key relationships.
b. Write programs to compute each of the queries in Exercise 3.10.
Answer:
a. The schema definitions can be written in two different ways, one of which is
a direct translation from the relational schema, while the other uses objectoriented features more directly.
• The first scheme is as follows:
class employee : public d Object {
public:
d String person-name;
d String street;
d String city;
};
class company : public d Object {
public:
d String company-name;
d String city;
};
class works : public d Object {
Exercises
public:
d Ref person;
d Ref comp;
d Long salary;
};
class manages : public d Object {
public:
d Ref person;
d Ref manager;
};
• The second schema is as follows
class employee : public d Object {
public:
d String person-name;
d String street;
d String city;
d Rel Ref comp;
d Ref manager;
d Long salary;
};
class company : public d Object {
public:
d String company-name;
d String city;
d Rel Set employees;
};
const char employees[] = ”employees”;
const char comp[] = ”comp”;
b. We present queries for the second schema.
• Find the company with the most employees.
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d Ref mostemployees(){
d Database emp db obj;
d Database * emp db = ”” emp db obj;
emp db− >open(”Emp-DB”);
d Transaction Trans;
Trans.begin();
d Extent all comps(emp db);
d Iterator> iter=all comps.create iterator();
d Iterator> iter2;
d Ref c, maxc;
d Ref e;
int count;
int maxcount=0;
while(iter.next(c)) {
iter2=(c− >employees).create iterator();
count=0;
while(iter2.next(e)) {
count++;
}
if(maxcount < count) {
maxcount=count;
maxc=c;
}
}
Trans.commit();
return maxc;
}
• Find the company with the smallest payroll.
Exercises
103
d Ref smallestpay(){
d Database emp db obj;
d Database * emp db = ”” emp db obj;
emp db− >open(”Emp-DB”);
d Transaction Trans;
Trans.begin();
d Extent all comps(emp db);
d Iterator> iter=all comps.create iterator();
d Iterator> iter2;
d Ref c, minc;
d Ref e;
d Long sal;
d Long minsal=0;
while(iter.next(c)) {
iter2=(c− >employees).create iterator();
sal=0;
while(iter2.next(e)) {
sal+=e− >salary;
}
if(minsal > sal) {
minsal=sal;
minc=c;
}
}
Trans.commit();
return minc;
}
• Find those companies whose employees earn a higher salary, on average, than the average salary at First Bank Corporation.
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d Set> highersal(){
d Database emp db obj;
d Database * emp db = ”” emp db obj;
emp db− >open(”Emp-DB”);
d Transaction Trans;
Trans.begin();
d Extent all comps(emp db);
d Iterator> iter=all comps.create iterator();
d Iterator> iter2;
d Ref c, FBC=all comps.select(company-name=”First Bank Corporation”);
d Set> result;
d Ref e;
int count;
d Long avsal=0, avFBCsal=0, sal=0;
iter2=(FBC− >employees).create iterator();
while(iter2.next(e)) {
count++;
sal+=e− >salary;
}
avFBCsal=sal/count;
while(iter.next(c)) {
iter2=(c− >employees).create iterator();
sal=0; count=0;
while(iter2.next(e)) {
sal+=e− >salary;
count++;
}
avsal=sal/count;
if(avsal > avFBCsal) {
result.insert element(c);
}
}
Trans.commit();
return result;
}
8.9 Using ODMG C++, give schema definitions corresponding to the E-R diagram in
Figure 2.29, using references to implement relationships.
Answer:
class person : public d Object {
public:
d String name;
d String address;
d String phone;
};
Exercises
class author : public person {
public:
d String URL;
d Rel Set books;
};
class publisher : public person {
public:
d String URL;
d Rel Set books;
};
class customer : public person {
public:
d String email;
d Rel Set baskets;
};
class book : public d Object {
public:
int year;
d String title;
float price;
d String ISBN;
d Rel Set authors;
d Rel Ref book publisher;
};
class shoppingbasket : public d Object {
public:
d String basketID;
d Rel Ref owner;
d Set> contains;
};
class warehouse : public d Object {
public:
d String address;
d String phone;
d String code;
d Set> stocks;
};
class book qty : public d Object {
public:
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};
d Ref book;
int number;
const char
const char
const char
const char
const char
books[] = ”books”;
authors[] = ”authors”;
book publisher[] = ”book publisher”;
baskets[] = ”baskets”;
owner[] = ”owner”;
8.10 Explain, using an example, how to represent a ternary relationship in an objectoriented data model such as ODMG C++.
Answer: To represent ternary relationships, create a class corresponding to the
relationship and refer to the entities in this class. For example, to represent the
ternary relationship in Figure 2.13, we do the following:
class workson : public d Object {
public:
d Ref emp;
d Ref branch;
d Ref job;
};
8.11 Explain how a persistent pointer is implemented. Contrast this implementation
with that of pointers as they exist in general-purpose languages, such as C or
Pascal.
Answer: Persistent pointers can be implemented as Abstract Data Types (ADTs).
These ADTs should provide the typical pointer operations like incrementing
and dereferencing, so their usage and regular pointer usage is uniform. Regular
pointers on the other hand are usually built-in types, implemented as part of
the language.
8.12 If an object is created without any references to it, how can that object be deleted?
Answer: If an object is created without any references to it, it can neither be
accessed nor deleted via a program. The only way is for the database system to
locate and delete such objects by itself. This is called garbage collection. One way
to do garbage collection is by the method of mark and sweep. First, the objects
referred to directly by programs are marked. Then references from these objects
to other objects are followed, and those referred objects are marked. This procedure is followed repeatedly until no more unmarked objects can be reached
by following reference chains from the marked objects. At this point, all these
remaining unmarked objects are deleted. This method is correct; we can prove
Exercises
107
that if no new objects are marked after a round of mark and sweep, the remaining unmarked objects are indeed unreferenced.
8.13 Consider a system that provides persistent objects. Is such a system necessarily
a database system? Explain your answer.
Answer: A database system must provide for such features as transactions,
queries (associative retrieval of objects), security, and integrity. A persistent object system may not offer such features.
C H A P T E R
9
Object-Relational Databases
This chapter describes extensions to relational database systems to provide complex
data types and object-oriented features. Such extended systems are called objectrelational systems. Since the chapter was introduced in the 3rd edition most commercial database systems have added some support for object-relational features, and
these features have been standardized as part of SQL:1999.
It would be instructive to assign students exercises aimed at finding applications
where the object-relational model, in particular complex objects, would be better
suited than the traditional relational model.
Changes from 3rd edition:
The query language features are now based on the SQL:1999 standard, which was
not ready when the 3rd edition was published; that edition was based from features
from several different proposals for extending SQL.
Exercises
9.1 Consider the database schema
Emp = (ename, setof(Children), setof(Skills))
Children = (name, Birthday)
Birthday = (day, month, year)
Skills = (type, setof(Exams))
Exams = (year, city)
Assume that attributes of type setof(Children), setof(Skills), and setof(Exams),
have attribute names ChildrenSet, SkillsSet, and ExamsSet, respectively. Suppose
the database contains a relation emp (Emp). Write the following queries in SQL:1999
(with the extensions described in this chapter).
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a. Find the names of all employees who have a child who has a birthday in
March.
b. Find those employees who took an examination for the skill type “typing”
in the city “Dayton”.
c. List all skill types in the relation emp.
Answer:
a. Find the names of all employees who have a child who has a birthday in
March.
select ename
from emp as e, e.ChildrenSet as c
where ’March’ in
(select birthday.month
from c
)
b. Find those employees who took an examination for the skill type “typing”
in the city “Dayton”.
select e.ename
from emp as e, e.SkillSet as s, s.ExamSet as x
where s.type = ’typing’ and x.city = ’Dayton’
c. List all skill types in the relation emp.
select distinct s.type
from emp as e, e.SkillSet as s
9.2 Redesign the database of Exercise 9.1 into first normal form and fourth normal
form. List any functional or multivalued dependencies that you assume. Also
list all referential-integrity constraints that should be present in the first- and
fourth-normal-form schemas.
Answer: To put the schema into first normal form, we flatten all the attributes
into a single relation schema.
Employee-details = (ename, cname, bday, bmonth, byear, stype, xyear, xcity)
We rename the attributes for the sake of clarity. cname is Children.name, and bday,
bmonth, byear are the Birthday attributes. stype is Skills.type, and xyear and xcity
are the Exams attributes. The FDs and multivalued dependencies we assume
are:ename, cname →
ename →
→
ename, stype →
→
bday, bmonth, byear
cname, bday, bmonth, byear
xyear, xcity
The FD captures the fact that a child has a unique birthday, under the assumption that one employee cannot have two children of the same name. The MVDs
capture the fact there is no relationship between the children of an employee
and his or her skills-information.
Exercises
111
The redesigned schema in fourth normal form is:Employee = (ename)
Child = (ename, cname, bday, bmonth, byear)
Skill = (ename, stype, xyear, xcity)
ename will be the primary key of Employee, and (ename, cname) will be the primary key of Child. The ename attribute is a foreign key in Child and in Skill,
referring to the Employee relation.
9.3 Consider the schemas for the table people, and the tables students and teachers,
which were created under people, in Section 9.3. Give a relational schema in third
normal form that represents the same information. Recall the constraints on subtables, and give all constraints that must be imposed on the relational schema
so that every database instance of the relational schema can also be represented
by an instance of the schema with inheritance.
Answer: A corresponding relational schema in third normal form is given below:People = (name, address)
Students = (name, degree, student-department)
Teachers = (name, salary, teacher-department)
name is the primary key for all the three relations, and it is also a foreign key
referring to People, for both Students and Teachers.
Instead of placing only the name attribute of People in Students and Teachers,
both its attributes can be included. In that case, there will be a slight change,
namely – (name, address) will become the foreign key in Students and Teachers.
The primary keys will remain the same in all tables.
9.4 A car-rental company maintains a vehicle database for all vehicles in its current
fleet. For all vehicles, it includes the vehicle identification number, license number, manufacturer, model, date of purchase, and color. Special data are included
for certain types of vehicles:
• Trucks: cargo capacity
• Sports cars: horsepower, renter age requirement
• Vans: number of passengers
• Off-road vehicles: ground clearance, drivetrain (four- or two-wheel drive)
Construct an SQL:1999 schema definition for this database. Use inheritance where
appropriate.
Answer: For this problem, we use table inheritance. We assume that MyDate,
Color and DriveTrainType are pre-defined types.
create type Vehicle
(vehicle-id integer,
license-number char(15),
manufacturer char(30),
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model char(30),
purchase-date MyDate,
color Color)
create table vehicle of type Vehicle
create table truck
(cargo-capacity integer)
under vehicle
create table sportsCar
(horsepower integer
renter-age-requirement integer)
under vehicle
create table van
(num-passengers integer)
under vehicle
create table offRoadVehicle
(ground-clearance real
driveTrain DriveTrainType)
under vehicle
9.5 Explain the distinction between a type x and a reference type ref(x). Under what
circumstances would you choose to use a reference type?
Answer: If the type of an attribute is x, then in each tuple of the table, corresponding to that attribute, there is an actual object of type x . If its type is ref(x),
then in each tuple, corresponding to that attribute, there is a reference to some
object of type x. We choose a reference type for an attribute, if that attribute’s
intended purpose is to refer to an independent object.
9.6 Consider the E-R diagram in Figure 2.11, which contains composite, multivalued
and derived attributes.
a. Give an SQL:1999 schema definition corresponding to the E-R diagram. Use
an array to represent the multivalued attribute, and appropriate SQL:1999
constructs to represent the other attribute types.
b. Give constructors for each of the structured types defined above.
Answer:
a. The corresponding SQL:1999 schema definition is given below. Note that the
derived attribute age has been translated into a method.
create type Name
Exercises
113
(first-name varchar(15),
middle-initial char,
last-name varchar(15))
create type Street
(street-name varchar(15),
street-number varchar(4),
apartment-number varchar(7))
create type Address
(street Street,
city varchar(15),
state varchar(15),
zip-code char(6))
create table customer
(name Name,
customer-id varchar(10),
address Adress,
phones char(7) array[10],
dob date)
method integer age()
b. create function Name (f varchar(15), m char, l varchar(15))
returns Name
begin
set first-name = f;
set middle-initial = m;
set last-name = l;
end
create function Street (sname varchar(15), sno varchar(4), ano varchar(7))
returns Street
begin
set street-name = sname;
set street-number = sno;
set apartment-number =ano;
end
create function Address (s Street, c varchar(15), sta varchar(15), zip varchar(6))
returns Address
begin
set street = s;
set city = c;
set state =sta;
set zip-code =zip;
end
9.7 Give an SQL:1999 schema definition of the E-R diagram in Figure 2.17, which
contains specializations.
Answer:
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create type Person
(name varchar(30),
street varchar(15),
city varchar(15))
create type Employee
under Person
(salary integer)
create type Customer
under Person
(credit-rating integer)
create type Officer
under Employee
(office-number integer)
create type Teller
under Employee
(station-number integer,
hours-worked integer)
create type Secretary
under Employee
(hours-worked integer)
create table person of Person
create table employee of Employee
under person
create table customer of Customer
under person
create table officer of Officer
under employee
create table teller of Teller
under employee
create table secretary of Secretary
under employee
9.8 Consider the relational schema shown in Figure 3.39.
a. Give a schema definition in SQL:1999 corresponding to the relational schema,
but using references to express foreign-key relationships.
b. Write each of the queries in Exercise 3.10 on the above schema, using SQL:1999.
Answer:
a. The schema definition is given below. Note that backward references can be
addedbut they are not so important as in OODBS because queries can be
written in SQL and joins can take care of integrity constraints.
create type Employee
(person-name varchar(30),
street varchar(15),
Exercises
115
city varchar(15))
create type Company
(company-name varchar(15),
(city varchar(15))
create table employee of Employee
create table company of Company
create type Works
(person ref(Employee) scope employee,
comp ref(Company) scope company,
salary int)
create table works of Works
create type Manages
(person ref(Employee) scope employee,
(manager ref(Employee) scope employee)
create table manages of Manages
b.
i. select comp− >name
from works
group by comp having count(person) ≥ all(select count(person)
from works
group by comp)
ii. select comp− >name
from works
group by comp having sum(salary) ≤ all(select sum(salary)
from works
group by comp)
iii. select comp− >name
from works
group by comp having avg(salary) > (select avg(salary)
from works
where comp− >company-name=”First Bank Corporation”)
9.9 Consider an employee database with two relations
employee (employee-name, street, city)
works (employee-name, company-name, salary)
where the primary keys are underlined. Write a query to find companies
whose employees earn a higher salary, on average, than the average salary at
First Bank Corporation.
a. Using SQL:1999 functions as appropriate.
b. Without using SQL:1999 functions.
Answer:
a. create function avg-salary(cname varchar(15))
returns integer
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declare result integer;
select avg(salary) into result
from works
where works.company-name = cname
return result;
end
select company-name
from works
where avg-salary(company-name) > avg-salary(”First Bank Corporation”)
b. select company-name
from works
group by company-name
having avg(salary) > (select avg(salary)
from works
where company-name=”First Bank Corporation”)
9.10 Rewrite the query in Section 9.6.1 that returns the titles of all books that have
more than one author, using the with clause in place of the function.
Answer:
with multauthors(title, count) as
select title, count(author)
from authors
group by title
select books4.title
from books4, multauthors
where books4.title = multauthors.title
and multauthors.count > 1
9.11 Compare the use of embedded SQL with the use in SQL of functions defined in
a general-purpose programming language. Under what circumstances would
you use each of these features?
Answer: SQL functions are primarily a mechanism for extending the power
of SQL to handle attributes of complex data types (like images), or to perform
complex and non-standard operations. Embedded SQL is useful when imperative actions like displaying results and interacting with the user are needed.
These cannot be done conveniently in an SQL only environment. Embedded
SQL can be used instead of SQL functions by retrieving data and then performing the function’s operations on the SQL result. However a drawback is that a
lot of query-evaluation functionality may end up getting repeated in the host
language code.
9.12 Suppose that you have been hired as a consultant to choose a database system
for your client’s application. For each of the following applications, state what
type of database system (relational, persistent-programming-language– based
Exercises
117
OODB, object relational; do not specify a commercial product) you would recommend. Justify your recommendation.
a. A computer-aided design system for a manufacturer of airplanes
b. A system to track contributions made to candidates for public office
c. An information system to support the making of movies
Answer:
a. A computer-aided design system for a manufacturer of airplanes :An OODB system would be suitable for this. That is because CAD requires complex data types, and being computation oriented, CAD tools are
typically used in a programming language environment needing to access
the database.
b. A system to track contributions made to candidates for public office :A relational system would be apt for this, as data types are expected to
be simple, and a powerful querying mechanism is essential.
c. An information system to support the making of movies :Here there will be extensive use of multimedia and other complex data
types. But queries are probably simple, and thus an object relational system
is suitable.
C H A P T E R
1 0
XML
In the 4 1/2 years since the previous edition was published, XML has gone from a little
known proposal to the World Wide Web Consortium, to an extensive set of standards
that are being used widely, and whose use is growing rapidly. In this period the goals
of XML have changed from being a better form SGML or HTML, into becoming the
primary data model for data interchange.
Our view of XML is decidedly database centric: it is important to be aware that
many uses of XML are document centric, but we believe the bulk of XML applications
will be in data representation and interchange between database applications. In this
view, XML is a data model that provides a number of features beyond that provided
by the relational model, in particular the ability to package related information into
a single unit, by using nested structures. Specific application domains for data representation and interchange need their own standards that define the data schema.
Given the extensive nature of XML and related standards, this chapter only attempts to provide an introduction, and does not attempt to provide a complete description. For a course that intends to explore XML in detail, supplementary material
may be required. These could include online information on XML and books on XML.
Exercises
10.1 Give an alternative representation of bank information containing the same
data as in Figure 10.1, but using attributes instead of subelements. Also give
the DTD for this representation.
Answer:
a. XML representation of data using attributes:
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b. DTD for the bank:
]>
10.2 Show, by giving a DTD, how to represent the books nested-relation from Section 9.1, using XML.
Answer:
Exercises
121
]>
10.3 Give the DTD for an XML representation of the following nested-relational
schema
Emp = (ename, ChildrenSet setof(Children), SkillsSet setof(Skills))
Children = (name, Birthday)
Birthday = (day, month, year)
Skills = (type, ExamsSet setof(Exams))
Exams = (year, city)
Answer:
]>
10.4 Write the following queries in XQuery, assuming the DTD from Exercise 10.3.
a. Find the names of all employees who have a child who has a birthday in
March.
b. Find those employees who took an examination for the skill type “typing”
in the city “Dayton”.
c. List all skill types in Emp.
Answer:
a. Find the names of all employees who have a child who has a birthday in
March.
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for $e in /db/emp,
$m in distinct($e/children/birthday/month)
where $m = ’March’
return $e/ename
b. Find those employees who took an examination for the skill type “typing”
in the city “Dayton”.
for $e in /db/emp
$s in $e/skills[type=’typing’]
$exam in $s/exams
where $exam/city= ’Dayton’
return $e/ename
c. Find those employees who took an examination for the skill type “typing”
in the city “Dayton”.
for $t in distinct (/db/emp/skills/type)
return $e/ename
10.5 Write queries in XSLT and in XPath on the DTD of Exercise 10.3 to list all skill
types in Emp.
Answer:
a. XPath: /db/emp/skills/type
b. XSLT:
10.6 Write a query in XQuery on the XML representation in Figure 10.1 to find the
total balance, across all accounts, at each branch. (Hint: Use a nested query to
get the effect of an SQL group by.)
Answer:
for $b in distinct (/bank/account/branch-name)
return
$b/text()
let $s := sum (/bank/account[branch-name=$b]/balance
return $s
Exercises
123
10.7 Write a query in XQuery on the XML representation in Figure 10.1 to compute
the left outer join of customer elements with account elements. (Hint: Use universal quantification.)
Answer:
for $b in /bank/account,
$c in /bank/customer,
$d in /bank/depositor
where $a/account-number = $d/account-number
and $c/customer-name = $d/customer-name
return $c $a
|
for $c in /bank/customer,
where every $d in /bank/depositor satisfies
(not ($c/customer-name=$d/customer-name))
return $c
10.8 Give a query in XQuery to flip the nesting of data from Exercise 10.2. That is, at
the outermost level of nesting the output must have elements corresponding to
authors, and each such element must have nested within it items corresponding to all the books written by the author.
Answer:
for $a in distinct (/bib/book/author)
return
$a/text()
for $b in (/bib/book/[author=$a])
return
$b/title
$b/publisher
$b/keyword
< \book>
< \author>
10.9 Give the DTD for an XML representation of the information in Figure 2.29. Create a separate element type to represent each relationship, but use ID and IDREF
to implement primary and foreign keys.
Answer: The answer is given in Figure 10.1.
10.10 Write queries in XSLT and XQuery to output customer elements with associated
account elements nested within the customer elements, given the bank infor-
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Chapter 10
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]>
Figure 10.1
XML DTD for Bookstore
Exercises
125
mation representation using ID and IDREFS in Figure 10.8.
Answer:
for $c in /bank/customer
return
$c/*
for $a in $c/id(@accounts)
return $a
10.11 Give a relational schema to represent bibliographical information specified as
per the DTD fragment in Figure 10.13. The relational schema must keep track
of the order of author elements. You can assume that only books and articles
appear as top level elements in XML documents.
Answer:
book (bid, title, year, publisher, place)
article (artid, title, journal, year, number, volume, pages)
book-author (bid, first-name,last-name, order)
article-author (artid, first-name,last-name, order)
10.12 Consider Exercise 10.11, and suppose that authors could also appear as top
level elements. What change would have to be done to the relational schema.
Answer:
book (bid, title, year, publisher, place)
article (artid, title, journal, year, number, volume, pages)
author (first-name, last-name)
book-author (bid, first-name, last-name, order)
article-author (artid, first-name,last-name, order)
10.13 Write queries in XQuery on the bibliography DTD fragment in Figure 10.13, to
do the following.
a. Find all authors who have authored a book and an article in the same year.
b. Display books and articles sorted by year.
c. Display books with more than one author.
Answer:
a. Find all authors who have authored a book and an article in the same year.
for $a in distinct (/bib/book/author)
$y in /bib/book[author=$a]/year
$art in /bib/article[author=$a and year=$y]
return $a
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· · · similar PCDATA declarations for year, publisher, place, journal, year,
number, volume, pages, last-name and first-name
]>
Figure 10.13. DTD for bibliographical data.
b. Display books and articles sorted by year.
for $a in ((/bib/book) | (/bib/article))
return $a sortby(year)
c. Display books with more than one author.
for $a in ((/bib/book[author/count()>1])
return $a
10.14 Show the tree representation of the XML data in Figure 10.1, and the representation of the tree using nodes and child relations described in Section 10.6.1.
Answer: The answer is given in Figure 10.2.
10.15 Consider the following recursive DTD.
]>
a. Give a small example of data corresponding to the above DTD.
b. Show how to map this DTD to a relational schema. You can assume that
part names are unique, that is, whereever a part appears, its subpart structure will be the same.
Answer:
a. Give a small example of data corresponding to the above DTD.
The answer is shown in Figure 10.3.
b. Show how to map this DTD to a relational schema.
part(partid,name)
subpartinfo(partid, subpartid, qty)
Attributes partid and subpartid of subpartinfo are foreign keys to part.
Exercises
nodes(1,element,bank,–)
nodes(2,element,account,–)
nodes(3,element,account,–)
nodes(4,element,account,–)
nodes(5,element,customer,–)
nodes(6,element,customer,–)
nodes(7,element,depositor,–)
nodes(8,element,depositor,–)
nodes(9,element,depositor,–)
child(2,1) child(3,1) child(4,1)
child(5,1) child(6,1)
child(7,1) child(8,1) child(9,1)
nodes(10,element,account-number,A-101)
nodes(11,element,branch-name,Downtown)
nodes(12,element,balance,500)
child(10,2) child(11,2) child(12,2)
nodes(13,element,account-number,A-102)
nodes(14,element,branch-name,Perryridge)
nodes(15,element,balance,400)
child(13,3) child(14,3) child(15,3)
nodes(16,element,account-number,A-201)
nodes(17,element,branch-name,Brighton)
nodes(18,element,balance,900)
child(16,4) child(17,4) child(18,4)
nodes(19,element,customer-name,Johnson)
nodes(20,element,customer-street,Alma)
nodes(21,element,customer-city,Palo Alto)
child(19,5) child(20,5) child(21,5)
nodes(22,element,customer-name,Hayes)
nodes(23,element,customer-street,Main)
nodes(24,element,customer-city,Harrison)
child(22,6) child(23,6) child(24,6)
nodes(25,element,account-number,A-101)
nodes(26,element,customer-name,Johnson)
child(25,7) child(26,7)
nodes(27,element,account-number,A-201)
nodes(28,element,customer-name,Johnson)
child(27,8) child(28,8)
nodes(29,element,account-number,A-102)
nodes(30,element,customer-name,Hayes)
child(29,9) child(30,9)
Figure 10.2
Relational Representation of XML Data as Trees
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bicycle
wheel
rim
1
spokes
40
tire
1
2
brake
2
gear
3
frame
1
Figure 10.3
Example Parts Data in XML
C H A P T E R
1 1
Storage and File Structure
This chapter presents basic file structure concepts. The chapter really consists of
two parts — the first dealing with relational databases, and the second with objectoriented databases. The second part can be omitted without loss of continuity for
later chapters.
Many computer science undergraduates have covered some of the material in this
chapter in a prior course on data structures or on file structures. Even if students’
backgrounds are primarily in data structures, this chapter is still important since it
addresses data structure issues as they pertain to disk storage. Buffer management issues, covered in Section 11.5.1 should be familiar to students who have taken an operating systems course. However, there are database-specific aspects of buffer management that make this section worthwhile even for students with an operating system
background.
Changes from 3rd edition:
The discussion of storage media, in particular magnetic disks (Section 11.2), has
been updated to reflect current technology. The section on RAID structures (Section 11.3)
has been improved with examples; the comparison of RAID levels has changed, since
disk drive capacity improvements have whittled away at the advantages of RAID 5.
Coverage of data dictionaries has been expanded.
Exercises
11.1 List the physical storage media available on the computers you use routinely.
Give the speed with which data can be accessed on each medium.
Answer: Your answer will be based on the computers and storage media that
you use. Typical examples would be hard disk, floppy disks and CD-ROM
drives.
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11.2 How does the remapping of bad sectors by disk controllers affect data-retrieval
rates?
Answer: Remapping of bad sectors by disk controllers does reduce data retrieval rates because of the loss of sequentiality amongst the sectors. But that is
better than the loss of data in case of no remapping!
11.3 Consider the following data and parity-block arrangement on four disks:
Disk 1
B1
P1
B8
..
.
Disk 2
B2
B5
P2
..
.
Disk 3
B3
B6
B9
..
.
Disk 4
B4
B7
B10
..
.
The Bi ’s represent data blocks; the Pi ’s represent parity blocks. Parity block Pi
is the parity block for data blocks B4i−3 to B4i . What, if any, problem might
this arrangement present?
Answer: This arrangement has the problem that Pi and B4i−3 are on the same
disk. So if that disk fails, reconstruction of B4i−3 is not possible, since data and
parity are both lost.
11.4 A power failure that occurs while a disk block is being written could result in
the block being only partially written. Assume that partially written blocks can
be detected. An atomic block write is one where either the disk block is fully
written or nothing is written (i.e., there are no partial writes). Suggest schemes
for getting the effect of atomic block writes with the following RAID schemes.
Your schemes should involve work on recovery from failure.
a. RAID level 1 (mirroring)
b. RAID level 5 (block interleaved, distributed parity)
Answer:
a. To ensure atomicity, a block write operation is carried out as follows:i. Write the information onto the first physical block.
ii. When the first write completes successfully, write the same information
onto the second physical block.
iii. The output is declared completed only after the second write completes
successfully.
During recovery, each pair of physical blocks is examined. If both are
identical and there is no detectable partial-write, then no further actions
are necessary. If one block has been partially rewritten, then we replace its
contents with the contents of the other block. If there has been no partialwrite, but they differ in content, then we replace the contents of the first
block with the contents of the second, or vice versa. This recovery procedure ensures that a write to stable storage either succeeds completely (that
is, updates both copies) or results in no change.
Exercises
131
The requirement of comparing every corresponding pair of blocks during recovery is expensive to meet. We can reduce the cost greatly by keeping track of block writes that are in progress, using a small amount of nonvolatile RAM. On recovery, only blocks for which writes were in progress
need to be compared.
b. The idea is similar here. For any block write, the information block is written first followed by the corresponding parity block. At the time of recovery, each set consisting of the nth block of each of the disks is considered. If none of the blocks in the set have been partially-written, and
the parity block contents are consistent with the contents of the information blocks, then no further action need be taken. If any block has been
partially-written, it’s contents are reconstructed using the other blocks. If
no block has been partially-written, but the parity block contents do not
agree with the information block contents, the parity block’s contents are
reconstructed.
11.5 RAID systems typically allow you to replace failed disks without stopping access to the system. Thus, the data in the failed disk must be rebuilt and written
to the replacement disk while the system is in operation. With which of the
RAID levels is the amount of interference between the rebuild and ongoing
disk accesses least? Explain your answer.
Answer: RAID level 1 (mirroring) is the one which facilitates rebuilding of a
failed disk with minimum interference with the on-going disk accesses. This is
because rebuilding in this case involves copying data from just the failed disk’s
mirror. In the other RAID levels, rebuilding involves reading the entire contents
of all the other disks.
11.6 Give an example of a relational-algebra expression and a query-processing
strategy in each of the following situations:
a. MRU is preferable to LRU.
b. LRU is preferable to MRU.
Answer:
a. MRU is preferable to LRU where R1 1 R2 is computed by using a nestedloop processing strategy where each tuple in R2 must be compared to each
block in R1 . After the first tuple of R2 is processed, the next needed block
is the first one in R1 . However, since it is the least recently used, the LRU
buffer management strategy would replace that block if a new block was
needed by the system.
b. LRU is preferable to MRU where R1 1 R2 is computed by sorting the relations by join values and then comparing the values by proceeding through
the relations. Due to duplicate join values, it may be necessary to “backup” in one of the relations. This “backing-up” could cross a block boundary into the most recently used block, which would have been replaced by
a system using MRU buffer management, if a new block was needed.
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Storage and File Structure
Under MRU, some unused blocks may remain in memory forever. In
practice, MRU can be used only in special situations like that of the nestedloop strategy discussed in example 0.a
11.7 Consider the deletion of record 5 from the file of Figure 11.8. Compare the
relative merits of the following techniques for implementing the deletion:
a. Move record 6 to the space occupied by record 5, and move record 7 to the
space occupied by record 6.
b. Move record 7 to the space occupied by record 5.
c. Mark record 5 as deleted, and move no records.
Answer:
a. Although moving record 6 to the space for 5, and moving record 7 to the
space for 6, is the most straightforward approach, it requires moving the
most records, and involves the most accesses.
b. Moving record 7 to the space for 5 moves fewer records, but destroys any
ordering in the file.
c. Marking the space for 5 as deleted preserves ordering and moves no records,
but requires additional overhead to keep track of all of the free space in the
file. This method may lead to too many “holes” in the file, which if not
compacted from time to time, will affect performance because of reduced
availability of contiguous free records.
11.8 Show the structure of the file of Figure 11.9 after each of the following steps:
a. Insert (Brighton, A-323, 1600).
b. Delete record 2.
c. Insert (Brighton, A-626, 2000).
Answer: (We use “↑ i” to denote a pointer to record “i”.)
The original file of Figure 11.9:
header
record 0
record 1
record 2
record 3
record 4
record 5
record 6
record 7
record 8
↑1
↑4
↑6
Perryridge
A-102 400
Mianus
Downtown
A-215 700
A-101 500
Perryridge
A-201 900
Downtown
Perryridge
A-110 600
A-218 700
a. The file after insert (Brighton, A-323, 1600).
Exercises
header
record 0
record 1
record 2
record 3
record 4
record 5
record 6
record 7
record 8
133
↑4
↑6
Perryridge
Brighton
Mianus
Downtown
A-102
A-323
A-215
A-101
400
1600
700
500
Perryridge
A-201 900
Downtown
Perryridge
A-110 600
A-218 700
b. The file after delete record 2.
header
record 0
record 1
record 2
record 3
record 4
record 5
record 6
record 7
record 8
↑2
↑4
↑6
Perryridge
Brighton
A-102 400
A-323 1600
Downtown
A-101 500
Perryridge
A-201 900
Downtown
Perryridge
A-110 600
A-218 700
The free record chain could have alternatively been from the header to
4, from 4 to 2, and finally from 2 to 6.
c. The file after insert (Brighton, A-626, 2000).
header
record 0
record 1
record 2
record 3
record 4
record 5
record 6
record 7
record 8
↑4
↑6
Perryridge
Brighton
Brighton
Downtown
A-102
A-323
A-626
A-101
400
1600
2000
500
Perryridge
A-201 900
Downtown
Perryridge
A-110 600
A-218 700
11.9 Give an example of a database application in which the reserved-space method
of representing variable-length records is preferable to the pointer method. Explain your answer.
Answer: In the reserved space method, a query comparing the last existing
field in a record to some value requires only one read from the disk. This single read is preferable to the potentially many reads needed to chase down the
pointers to the last field if the pointer method is used.
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Chapter 11
Storage and File Structure
11.10 Give an example of a database application in which the pointer method of representing variable-length records is preferable to the reserved-space method.
Explain your answer.
Answer: Using the pointer method, a join operation on attributes which are
only in the anchor block can be performed on only this smaller amount of data,
rather than on the entire relation, as would be the case using the reserved space
method. Therefore, in this join example, the pointer method is preferable.
11.11 Show the structure of the file of Figure 11.12 after each of the following steps:
a. Insert (Mianus, A-101, 2800).
b. Insert (Brighton, A-323, 1600).
c. Delete (Perryridge, A-102, 400).
Answer:
a. insert (Mianus, A-101, 2800) changes record 2 to:
2
Mianus
A-215
700
A-101
2800
⊥
⊥
b. insert (Brighton, A-323, 1600) changes record 5 to:
5
Brighton
A-216
750
A-323
1600
⊥
⊥
c. delete (Perryridge, A-102, 400) changes record 0 to:
0
Perryridge
A-102
900
A-218
700
⊥
⊥
Exercises
135
11.12 What happens if you attempt to insert the record
(Perryridge, A-929, 3000)
into the file of Figure 11.12?
Answer: Inserting (Perryridge, A-929, 3000) into the file of Figure 11.12 causes
an error because the Perryridge record has exceeded the maximum length reserved.
11.13 Show the structure of the file of Figure 11.13 after each of the following steps:
a. Insert (Mianus, A-101, 2800).
b. Insert (Brighton, A-323, 1600).
c. Delete (Perryridge, A-102, 400).
Answer:
a. The figure after insert (Mianus, A-101, 2800).
0
1
2
3
4
5
6
7
8
9
↑5
↑9
↑7
↑8
Perryridge
Round Hill
Mianus
Downtown
Redwood
Brighton
A-102
A-305
A-215
A-101
A-222
A-201
A-216
A-110
A-218
A-101
400
350
700
500
700
900
750
600
700
2800
b. The figure after insert (Brighton, A-323, 1600).
0
1
2
3
4
5
6
7
8
9
10
↑5
↑9
↑7
↑8
↑ 10
Perryridge
Round Hill
Mianus
Downtown
Redwood
Brighton
A-102
A-305
A-215
A-101
A-222
A-201
A-216
A-110
A-218
A-101
A-323
400
350
700
500
700
900
750
600
700
2800
1600
c. The figure after delete (Perryridge, A-102, 400).
136
Chapter 11
Storage and File Structure
1
2
3
4
5
6
7
8
9
10
↑9
↑7
↑8
↑ 10
Round Hill
Mianus
Downtown
Redwood
Perryridge
Brighton
A-305
A-215
A-101
A-222
A-201
A-216
A-110
A-218
A-101
A-323
350
700
500
700
900
750
600
700
2800
1600
11.14 Explain why the allocation of records to blocks affects database-system performance significantly.
Answer: If we allocate related records to blocks, we can often retrieve most,
or all, of the requested records by a query with one disk access. Disk accesses
tend to be the bottlenecks in databases; since this allocation strategy reduces
the number of disk accesses for a given operation, it significantly improves
performance.
11.15 If possible, determine the buffer-management strategy used by the operating
system running on your local computer system, and what mechanisms it provides to control replacement of pages. Discuss how the control on replacement
that it provides would be useful for the implementation of database systems.
Answer: The typical OS uses LRU for buffer replacement. This is often a bad
strategy for databases. As explained in Section 11.5.2 of the text, MRU is the
best strategy for nested loop join. In general no single strategy handles all scenarios well, and ideally the database system should be given its own buffer
cache for which the replacement policy takes into account all the performance
related issues.
11.16 In the sequential file organization, why is an overflow block used even if there
is, at the moment, only one overflow record?
Answer: An overflow block is used in sequential file organization because a
block is the smallest space which can be read from a disk. Therefore, using any
smaller region would not be useful from a performance standpoint. The space
saved by allocating disk storage in record units would be overshadowed by
the performance cost of allowing blocks to contain records of multiple files.
11.17 List two advantages and two disadvantages of each of the following strategies
for storing a relational database:
a. Store each relation in one file.
b. Store multiple relations (perhaps even the entire database) in one file.
Answer:
a. Advantages of storing a relation as a file include using the file system provided by the OS , thus simplifying the DBMS, but incurs the disadvantage
Exercises
137
of restricting the ability of the DBMS to increase performance by using more
sophisticated storage structures.
b. By using one file for the entire database, these complex structures can be
implemented through the DBMS, but this increases the size and complexity
of the DBMS.
11.18 Consider a relational database with two relations:
course (course-name, room, instructor)
enrollment (course-name, student-name, grade)
Define instances of these relations for three courses, each of which enrolls five
students. Give a file structure of these relations that uses clustering.
course relation
course-name
room
instructor
Pascal
CS-101 Calvin, B c1
Answer:
C
CS-102 Calvin, B c2
LISP
CS-102
Kess, J
c3
enrollment relation
course-name student-name grade
Pascal
Carper, D
A
Pascal
Merrick, L
A
Pascal
Mitchell, N
B
Pascal
Bliss, A
C
Pascal
Hames, G
C
C
Nile, M
A
C
Mitchell, N
B
C
Carper, D
A
C
Hurly, I
B
C
Hames, G
A
Lisp
Bliss, A
C
Lisp
Hurly, I
B
Lisp
Nile, M
D
Lisp
Stars, R
A
Lisp
Carper, D
A
e1
e2
e3
e4
e5
e6
e7
e8
e9
e10
e11
e12
e13
e14
e15
Block 0 contains: c1 , e1 , e2 , e3 , e4 , and e5
Block 1 contains: c2 , e6 , e7 , e8 , e9 and e10
Block 2 contains: c3 , e11 , e12 , e13 , e14 , and e15
11.19 Consider the following bitmap technique for tracking free space in a file. For
each block in the file, two bits are maintained in the bitmap. If the block is
between 0 and 30 percent full the bits are 00, between 30 and 60 percent the
bits are 01, between 60 and 90 percent the bits are 10, and above 90 percent the
bits are 11. Such bitmaps can be kept in memory even for quite large files.
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Chapter 11
Storage and File Structure
a. Describe how to keep the bitmap up-to-date on record insertions and deletions.
b. Outline the benefit of the bitmap technique over free lists when searching
for free space and when updating free space information.
Answer:
a. Everytime a record is inserted/deleted, check if the usage of the block has
changed levels. In that case, update the corrosponding bits.
b. If free space for n records is required, then in free lists technique, n accesses
of the list of free records are required. However, in bitmap technique, a
block with free space for n recores (or more that one blocks if required) can
be directly found out. The free space thus obtained is also more contiguous
than that obtained by free list technique.
11.20 Give a normalized version of the Index-metadata relation, and explain why using the normalized version would result in worse performance.
Answer: The Index-metadata relation can be normalized as follows
Index-metadata (index-name, relation-name, index-type, attrib-set)
Attribset-metadata (relation-name, attrib-set, attribute-name)
Though the normalized version will have less space requirements, but it will
require extra disk accesses to read Attribset-metadata everytime an index has
to be accessed. Thus, it will lead to worse performance.
11.21 Explain why a physical OID must contain more information than a pointer to a
physical storage location.
Answer: A physical OID needs to have a unique identifier in addition to a
pointer to a physical storage location. This is required to prevent dereferences
of dangling pointers.
11.22 If physical OIDs are used, an object can be relocated by keeping a forwarding
pointer to its new location. In case an object gets forwarded multiple times,
what would be the effect on retrieval speed? Suggest a technique to avoid multiple accesses in such a case.
Answer: If an object gets forwarded multiple times, the retrieval speed will
decrease because accessing it will require accessing the series of locations from
which the object has been successively forwarded to the current location.
Multiple accesses can be avoided by always keeping in the oldest location
the latest address of the object. This can be done by checking while forwarding
whether this object has already been forwarded and in that case updating the
forwarding address at the oldest location. Thus, atmost two accesses will be
required.
11.23 Define the term dangling pointer. Describe how the unique-id scheme helps in
detecting dangling pointers in an object-oriented database.
Exercises
139
Answer: A dangling pointer is a pointer to an area which no longer contains
valid data.
In the unique-id scheme to detect dangling pointers, physical OIDs may contain a unique identifier which is an integer that distinguishes the OID from the
identifiers of other objects that happened to be stored at the same location earlier, and were deleted or moved elsewhere. The unique identifier is also stored
with the object, and the identifiers in an OID and the corresponding object
should match. If the unique identifier in a physical OID does not match the
unique identifier in the object to which that OID points, the system detects that
the pointer is a dangling pointer, and signals an error.
11.24 Consider the example on page 435, which shows that there is no need for
deswizzling if hardware swizzling is used. Explain why, in that example, it
is safe to change the short identifier of page 679.34278 from 2395 to 5001. Can
some other page already have short identifier 5001? If it could, how can you
handle that situation?
Answer: While swizzling, if the short identifier of page 679.34278 is changed
from 2395 to 5001, it is either because
a. the system discovers that 679.34278 has already been allocated the virtualmemory page 5001 in some previous step, or else
b. 679.34278 has not been allocated any virtual memory page so far, and the
free virtual memory page 5001 is now allocated to it.
Thus in either case, it cannot be true that the current page already uses the
same short identifier 5001 to refer to some database page other than 679.34278.
Some other page may use 5001 to refer to a different database page, but then
each page has its own independent mapping from short to full page identifiers,
so this is all right.
Note that if we do swizzling as described in the text, and different processes
need simultaneous access to a database page, they will have to map separate
copies of the page to their individual virtual address spaces. Extensions to the
scheme are possible to avoid this.
C H A P T E R
1 2
Indexing and Hashing
This chapter covers indexing techniques ranging from the most basic one to highly
specialized ones. Due to the extensive use of indices in database systems, this chapter
constitutes an important part of a database course.
A class that has already had a course on data-structures would likely be familiar
with hashing and perhaps even B+ -trees. However, this chapter is necessary reading
even for those students since data structures courses typically cover indexing in main
memory. Although the concepts carry over to database access methods, the details
(e.g., block-sized nodes), will be new to such students.
The sections on B-trees (Sections 12.4), grid files (Section 12.9.3) and bitmap indexing (Section 12.9.4) may be omitted if desired.
Changes from 3rd edition:
The description of querying on B+ -trees has been augmented with pseudo-code. The
pseudo-code for insertion on B+ -trees has been simplified. The section on index definition in SQL (Section 12.8) is new to this edition, as is the coverage of bitmap indices
(Section 12.9.4).
Exercises
12.1 When is it preferable to use a dense index rather than a sparse index? Explain
your answer.
Answer: It is preferable to use a dense index instead of a sparse index when
the file is not sorted on the indexed field (such as when the index is a secondary
index) or when the index file is small compared to the size of memory.
12.2 Since indices speed query processing, why might they not be kept on several
search keys? List as many reasons as possible.
Answer: Reasons for not keeping several search indices include:
141
142
Chapter 12
Indexing and Hashing
a. Every index requires additional CPU time and disk I/O overhead during
inserts and deletions.
b. Indices on non-primary keys might have to be changed on updates, although an index on the primary key might not (this is because updates
typically do not modify the primary key attributes).
c. Each extra index requires additional storage space.
d. For queries which involve conditions on several search keys, efficiency
might not be bad even if only some of the keys have indices on them.
Therefore database performance is improved less by adding indices when
many indices already exist.
12.3 What is the difference between a primary index and a secondary index?
Answer: The primary index is on the field which specifies the sequential order of the file. There can be only one primary index while there can be many
secondary indices.
12.4 Is it possible in general to have two primary indices on the same relation for
different search keys? Explain your answer.
Answer: In general, it is not possible to have two primary indices on the same
relation for different keys because the tuples in a relation would have to be
stored in different order to have same values stored together. We could accomplish this by storing the relation twice and duplicating all values, but for a
centralized system, this is not efficient.
12.5 Construct a B+ -tree for the following set of key values:
(2, 3, 5, 7, 11, 17, 19, 23, 29, 31)
Assume that the tree is initially empty and values are added in ascending order. Construct B+ -trees for the cases where the number of pointers that will fit
in one node is as follows:
a. Four
b. Six
c. Eight
Answer: The following were generated by inserting values into the B+ -tree in
ascending order. A node (other than the root) was never allowed to have fewer
than n/2! values/pointers.
a.
19
5
2
b.
3
5
7
11
29
11
17
19
23
29
31
143
Exercises
2
3
5
c.
7
19
7
11 17
19
23 29
23
29
31
11
2
3
5
7
11
17
19
31
12.6 For each B+ -tree of Exercise 12.5, show the steps involved in the following
queries:
a. Find records with a search-key value of 11.
b. Find records with a search-key value between 7 and 17, inclusive.
Answer:
With structure 0.a:
a. Find records with a value of 11
i. Search the first level index; follow the first pointer.
ii. Search next level; follow the third pointer.
iii. Search leaf node; follow first pointer to records with key value 11.
b. Find records with value between 7 and 17 (inclusive)
i. Search top index; follow first pointer.
ii. Search next level; follow second pointer.
iii. Search third level; follow second pointer to records with key value 7,
and after accessing them, return to leaf node.
iv. Follow fourth pointer to next leaf block in the chain.
v. Follow first pointer to records with key value 11, then return.
vi. Follow second pointer to records with with key value 17.
With structure 0.b:
a. Find records with a value of 11
i. Search top level; follow second pointer.
ii. Search next level; follow second pointer to records with key value 11.
b. Find records with value between 7 and 17 (inclusive)
i. Search top level; follow second pointer.
ii. Search next level; follow first pointer to records with key value 7, then
return.
iii. Follow second pointer to records with key value 11, then return.
iv. Follow third pointer to records with key value 17.
With structure 0.c:
a. Find records with a value of 11
i. Search top level; follow second pointer.
ii. Search next level; follow first pointer to records with key value 11.
b. Find records with value between 7 and 17 (inclusive)
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Chapter 12
Indexing and Hashing
i. Search top level; follow first pointer.
ii. Search next level; follow fourth pointer to records with key value 7,
then return.
iii. Follow eighth pointer to next leaf block in chain.
iv. Follow first pointer to records with key value 11, then return.
v. Follow second pointer to records with key value 17.
12.7 For each B+ -tree of Exercise 12.5, show the form of the tree after each of the
following series of operations:
a.
b.
c.
d.
e.
Insert 9.
Insert 10.
Insert 8.
Delete 23.
Delete 19.
Answer:
• With structure 0.a:
Insert 9:
19
5
2
3
5
7
11
29
9
11
17
19
23
29
31
Insert 10:
19
5
2
3
5
7
9
9
11
29
10
11
17
19
23
29
31
19
23
29
31
Insert 8:
19
5
2
3
5
Delete 23:
7
8
9
9
11
10
29
11
17
145
Exercises
11
5
2
3
5
19
9
7
8
9
10
11
17
19
29
31
29
31
Delete 19:
11
5
2
3
5
9
7
29
8
9
10
11
17
• With structure 0.b:
Insert 9:
2
3
5
7
19
7
9
7
19
7
9
11 17
19
23 29
31
10
19
23 29
31
Insert 10:
2
3
5
11 17
Insert 8:
7
2
3
5
7
8
10 19
9
11 17
10
19
23 29
Delete 23:
7
2
3
5
7
8
10
9
19
10
11 17
19
29
Delete 19:
2
3
5
• With structure 0.c:
7
10
7
8
9
10
11 17
29
31
31
31
146
Chapter 12
Indexing and Hashing
Insert 9:
11
2
3
5
7
9
11
17 19
23
29
31
11
17 19
23
29
31
11
17 19
23
29
31
Insert 10:
11
2
3
5
7
9
10
Insert 8:
11
2
3
5
7
8
9
10
Delete 23:
11
2
3
5
7
8
9
10
11
17 19
29
31
Delete 19:
11
2
3
5
7
8
9
10
11
17
29
31
12.8 Consider the modified redistribution scheme for B+ -trees described in page
463. What is the expected height of the tree as a function of n?
Answer: If there are K search-key values and m − 1 siblings are involved in
the redistribution, the expected height of the tree is: log(m−1)n/m (K)
12.9 Repeat Exercise 12.5 for a B-tree.
Answer: The algorithm for insertion into a B-tree is:
Locate the leaf node into which the new key-pointer pair should be inserted.
If there is space remaining in that leaf node, perform the insertion at the correct
location, and the task is over. Otherwise insert the key-pointer pair conceptually into the correct location in the leaf node, and then split it along the middle.
The middle key-pointer pair does not go into either of the resultant nodes of
the split operation. Instead it is inserted into the parent node, along with the
tree pointer to the new child. If there is no space in the parent, a similar procedure is repeated.
The deletion algorithm is:
Exercises
147
Locate the key value to be deleted, in the B-tree.
a. If it is found in a leaf node, delete the key-pointer pair, and the record
from the file. If the leaf node contains less than n/2! − 1 entries as a result
of this deletion, it is either merged with its siblings, or some entries are
redistributed to it. Merging would imply a deletion, whereas redistribution
would imply change(s) in the parent node’s entries. The deletions may
ripple upto the root of the B-tree.
b. If the key value is found in an internal node of the B-tree, replace it and
its record pointer by the smallest key value in the subtree immediately to
its right and the corresponding record pointer. Delete the actual record in
the database file. Then delete that smallest key value-pointer pair from the
subtree. This deletion may cause further rippling deletions till the root of
the B-tree.
Below are the B-trees we will get after insertion of the given key values.
We assume that leaf and non-leaf nodes hold the same number of search key
values.
a.
5
2
29
? ? ? XX
9
+ ZZ~ XXXX
z
7 11
3
??
19 23
??
b.
7
2
17
??
31
?
23
? ? XXXXXX
XXXz
?
X
3
11 17 19
5
???
???
c.
29 31
??
11
2
3
5
7
17 19 23 29 31
12.10 Explain the distinction between closed and open hashing. Discuss the relative
merits of each technique in database applications.
Answer: Open hashing may place keys with the same hash function value in
different buckets. Closed hashing always places such keys together in the same
bucket. Thus in this case, different buckets can be of different sizes, though the
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Chapter 12
Indexing and Hashing
implementation may be by linking together fixed size buckets using overflow
chains. Deletion is difficult with open hashing as all the buckets may have to
inspected before we can ascertain that a key value has been deleted, whereas
in closed hashing only that bucket whose address is obtained by hashing the
key value need be inspected. Deletions are more common in databases and
hence closed hashing is more appropriate for them. For a small, static set of
data lookups may be more efficient using open hashing. The symbol table of a
compiler would be a good example.
12.11 What are the causes of bucket overflow in a hash file organization? What can
be done to reduce the occurrence of bucket overflows?
Answer: The causes of bucket overflow are :a. Our estimate of the number of records that the relation will have was too
low, and hence the number of buckets allotted was not sufficient.
b. Skew in the distribution of records to buckets. This may happen either because there are many records with the same search key value, or because
the the hash function chosen did not have the desirable properties of uniformity and randomness.
To reduce the occurrence of overflows, we can :a. Choose the hash function more carefully, and make better estimates of the
relation size.
b. If the estimated size of the relation is nr and number of records per block is
fr , allocate (nr /fr ) ∗ (1 + d) buckets instead of (nr /fr ) buckets. Here d is a
fudge factor, typically around 0.2. Some space is wasted: About 20 percent
of the space in the buckets will be empty. But the benefit is that some of the
skew is handled and the probability of overflow is reduced.
12.12 Suppose that we are using extendable hashing on a file that contains records
with the following search-key values:
2, 3, 5, 7, 11, 17, 19, 23, 29, 31
Show the extendable hash structure for this file if the hash function is h(x) = x
mod 8 and buckets can hold three records.
Answer:
Exercises
149
2
17
3
3
2
000
001
010
3
3
11
19
011
100
101
2
5
29
110
111
2
7
23
31
12.13 Show how the extendable hash structure of Exercise 12.12 changes as the result
of each of the following steps:
a.
b.
c.
d.
Delete 11.
Delete 31.
Insert 1.
Insert 15.
Answer:
a. Delete 11: From the answer to Exercise 12.12, change the third bucket to:
3
3
19
At this stage, it is possible to coalesce the second and third buckets. Then it
is enough if the bucket address table has just four entries instead of eight.
For the purpose of this answer, we do not do the coalescing.
b. Delete 31: From the answer to 12.12, change the last bucket to:
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Chapter 12
Indexing and Hashing
2
7
23
c. Insert 1: From the answer to 12.12, change the first bucket to:
2
1
17
d. Insert 15: From the answer to 12.12, change the last bucket to:
2
7
15
23
12.14 Give pseudocode for deletion of entries from an extendable hash structure,
including details of when and how to coalesce buckets. Do not bother about
reducing the size of the bucket address table.
Answer: Let i denote the number of bits of the hash value used in the hash
table. Let BSIZE denote the maximum capacity of each bucket.
Exercises
151
delete(value Kl )
begin
j = first i high-order bits of h(Kl );
delete value Kl from bucket j;
coalesce(bucket j);
end
coalesce(bucket j)
begin
ij = bits used in bucket j;
k = any bucket with first (ij − 1) bits same as that
of bucket j while the bit ij is reversed;
ik = bits used in bucket k;
if(ij = ik )
return; /* buckets cannot be merged */
if(entries in j + entries in k > BSIZE)
return; /* buckets cannot be merged */
move entries of bucket k into bucket j;
decrease the value of ij by 1;
make all the bucket-address-table entries,
which pointed to bucket k, point to j;
coalesce(bucket j);
end
Note that we can only merge two buckets at a time. The common hash prefix
of the resultant bucket will have length one less than the two buckets merged.
Hence we look at the buddy bucket of bucket j differing from it only at the last
bit. If the common hash prefix of this bucket is not ij , then this implies that the
buddy bucket has been further split and merge is not possible.
When merge is successful, further merging may be possible, which is handled by a recursive call to coalesce at the end of the function.
12.15 Suggest an efficient way to test if the bucket address table in extendable hashing can be reduced in size, by storing an extra count with the bucket address
table. Give details of how the count should be maintained when buckets are
split, coalesced or deleted.
(Note: Reducing the size of the bucket address table is an expensive operation, and subsequent inserts may cause the table to grow again. Therefore, it
is best not to reduce the size as soon as it is possible to do so, but instead do
it only if the number of index entries becomes small compared to the bucket
address table size.)
Answer: If the hash table is currently using i bits of the hash value, then maintain a count of buckets for which the length of common hash prefix is exactly
i.
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Consider a bucket j with length of common hash prefix ij . If the bucket is
being split, and ij is equal to i, then reset the count to 1. If the bucket is being
split and ij is one less that i, then increase the count by 1. It the bucket if being
coalesced, and ij is equal to i then decrease the count by 1. If the count becomes
0, then the bucket address table can be reduced in size at that point.
However, note that if the bucket address table is not reduced at that point,
then the count has no significance afterwards. If we want to postpone the reduction, we have to keep an array of counts, i.e. a count for each value of common hash prefix. The array has to be updated in a similar fashion. The bucket
address table can be reduced if the ith entry of the array is 0, where i is the
number of bits the table is using. Since bucket table reduction is an expensive
operation, it is not always advisable to reduce the table. It should be reduced
only when sufficient number of entries at the end of count array become 0.
12.16 Why is a hash structure not the best choice for a search key on which range
queries are likely?
Answer: A range query cannot be answered efficiently using a hash index,
we will have to read all the buckets. This is because key values in the range do
not occupy consecutive locations in the buckets, they are distributed uniformly
and randomly throughout all the buckets.
12.17 Consider a grid file in which we wish to avoid overflow buckets for performance reasons. In cases where an overflow bucket would be needed, we instead reorganize the grid file. Present an algorithm for such a reorganization.
Answer: Let us consider a two-dimensional grid array. When a bucket overflows, we can split the ranges corresponding to that row and column into two,
in both the linear scales. Thus the linear scales will get one additional entry
each, and the bucket is split into four buckets. The ranges should be split in
such a way as to ensure that the four resultant buckets have nearly the same
number of values.
There can be several other heuristics for deciding how to reorganize the
ranges, and hence the linear scales and grid array.
12.18 Consider the account relation shown in Figure 12.25.
a. Construct a bitmap index on the attributes branch-name and balance, dividing balance values into 4 ranges: below 250, 250 to below 500, 500 to below
750, and 750 and above.
b. Consider a query that requests all accounts in Downtown with a balance of
500 or more. Outline the steps in answering the query, and show the final
and intermediate bitmaps constructed to answer the query.
Answer: We reproduce the account relation of Figure 12.25 below.
Exercises
A-217
A-101
A-1 10
A-215
A-102
A-201
A-218
A-222
A-305
Bitmaps for branch-name
Brighton
1 0 0 0
Downtown 0 1 1 0
Mianus
0 0 0 1
Perryridge 0 0 0 0
Redwood
0 0 0 0
Round hill 0 0 0 0
Bitmaps for balance
L1
L2
L3
L4
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
Brighton
Downtown
Downtown
Mianus
Perryridge
Perryridge
Perryridge
Redwood
Round Hill
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
153
750
500
600
700
400
900
700
700
350
0
0
0
0
0
1
0
1
0
0
where, level L1 is below 250, level L2 is from 250 to below 500, L3 from 500
to below 750 and level L4 is above 750.
To find all accounts in Downtown with a balance of 500 or more, we find the
union of bitmaps for levels L3 and L4 and then intersect it with the bitmap for
Downtown.
Downtown
L3
L4
L3 ∪ L4
Downtown
Downtown ∩(L3 ∪ L4 )
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
Thus, the required tuples are A-101 and A-110.
12.19 Show how to compute existence bitmaps from other bitmaps. Make sure that
your technique works even in the presence of null values, by using a bitmap
for the value null.
Answer: The existence bitmap for a relation can be calculated by taking the
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Indexing and Hashing
union (logical-or) of all the bitmaps on that attribute, including the bitmap for
value null.
12.20 How does data encryption affect index schemes? In particular, how might it
affect schemes that attempt to store data in sorted order?
Answer: Note that indices must operate on the encrypted data or someone
could gain access to the index to interpret the data. Otherwise, the index would
have to be restricted so that only certain users could access it. To keep the data
in sorted order, the index scheme would have to decrypt the data at each level
in a tree. Note that hash systems would not be affected.
C H A P T E R
1 3
Query Processing
This chapter describes the process by which queries are executed efficiently by a
database system. The chapter starts off with measures of cost, then proceeds to algorithms for evaluation of relational algebra operators and expressions. This chapter
applies concepts from Chapters 3, 11, and 12.
Changes from 3rd edition:
The single chapter on query processing in the previous edition has been replaced
by two chapters, the first on query processing and the second on query optimization.
Another significant change is the separation of size estimation from the presentation
of query processing algorithms.
As a result, of these changes, query processing algorithms can be covered without
tedious and distracting details of size estimation. Although size estimation is covered
later, in Chapter 14, the presentation there has been simplified by omitting some details. Instructors can choose to cover query processing but omit query optimization,
without loss of continuity with later chapters.
Exercises
13.1 Why is it not desirable to force users to make an explicit choice of a queryprocessing strategy? Are there cases in which it is desirable for users to be
aware of the costs of competing query-processing strategies? Explain your answer.
Answer: In general it is not desirable to force users to choose a query processing strategy because naive users might select an inefficient strategy. The
reason users would make poor choices about processing queries is that they
would not know how a relation is stored, nor about its indices. It is unreasonable to force users to be aware of these details since ease of use is a major object
155
156
Chapter 13
Query Processing
of database query languages. If users are aware of the costs of different strategies they could write queries efficiently, thus helping performance. This could
happen if experts were using the system.
13.2 Consider the following SQL query for our bank database:
select T.branch-name
from branch T, branch S
where T.assets > S.assets and S.branch-city = “Brooklyn”
Write an efficient relational-algebra expression that is equivalent to this query.
Justify your choice.
Answer:
ΠT.branch-name ((Πbranch-name, assets (ρT (branch))) 1T.assets>S.assets
(Πassets (σ(branch-city = “Brooklyn”) (ρS (branch)))))
This expression performs the theta join on the smallest amount of data possible. It does this by restricting the right hand side operand of the join to only
those branches in Brooklyn, and also eliminating the unneeded attributes from
both the operands.
13.3 What are the advantages and disadvantages of hash indices relative to B+ -tree
indices? How might the type of index available influence the choice of a queryprocessing strategy?
Answer: Hash indices enable us to perform point lookup (eg. σA=r (relation))
operations very fast, but for range searches the B+ -tree index would be much
more efficient. If there is a range query to be evaluated, and only a hash index
is available, the better strategy might be to perform a file scan rather than using
that index.
13.4 Assume (for simplicity in this exercise) that only one tuple fits in a block and
memory holds at most 3 page frames. Show the runs created on each pass of
the sort-merge algorithm, when applied to sort the following tuples on the first
attribute: (kangaroo, 17), (wallaby, 21), (emu, 1), (wombat, 13), (platypus, 3),
(lion, 8), (warthog, 4), (zebra, 11), (meerkat, 6), (hyena, 9), (hornbill, 2), (baboon,
12).
Answer: We will refer to the tuples (kangaroo, 17) through (baboon, 12) using
tuple numbers t1 through t12 . We refer to the j th run used by the ith pass, as
rij . The initial sorted runs have three blocks each. They are:r11
=
{t3 , t1 , t2 }
r12
r13
=
=
{t6 , t5 , t4 }
{t9 , t7 , t8 }
r14
=
{t12 , t11 , t10 }
Exercises
157
Each pass merges three runs. Therefore the runs after the end of the first pass
are:r21
r22
=
=
{t3 , t1 , t6 , t9 , t5 , t2 , t7 , t4 , t8 }
{t12 , t11 , t10 }
At the end of the second pass, the tuples are completely sorted into one run:r31
= {t12 , t3 , t11 , t10 , t1 , t6 , t9 , t5 , t2 , t7 , t4 , t8 }
13.5 Let relations r1 (A, B, C) and r2 (C, D, E) have the following properties: r1 has
20,000 tuples, r2 has 45,000 tuples, 25 tuples of r1 fit on one block, and 30 tuples
of r2 fit on one block. Estimate the number of block accesses required, using
each of the following join strategies for r1 1 r2 :
a.
b.
c.
d.
Nested-loop join
Block nested-loop join
Merge join
Hash join
Answer: r1 needs 800 blocks, and r2 needs 1500 blocks. Let us assume M pages
of memory. If M > 800, the join can easily be done in 1500 + 800 disk accesses,
using even plain nested-loop join. So we consider only the case where M ≤ 800
pages.
a. Nested-loop join:
Using r1 as the outer relation we need 20000 ∗ 1500 + 800 = 30, 000, 800
disk accesses, if r2 is the outer relation we need 45000 ∗ 800 + 1500 =
36, 001, 500 disk accesses.
b. Block nested-loop join:
800
! ∗ 1500 + 800 disk accesses, if
If r1 is the outer relation, we need M−1
1500
r2 is the outer relation we need M−1 ! ∗ 800 + 1500 disk accesses.
c. Merge-join:
Assuming that r1 and r2 are not initially sorted on the join key, the total
sorting cost inclusive of the output is Bs = 1500(2 logM−1(1500/M )! +
2) + 800(2 logM−1(800/M )! + 2) disk accesses. Assuming all tuples with
the same value for the join attributes fit in memory, the total cost is Bs +
1500 + 800 disk accesses.
d. Hash-join:
We assume no overflow occurs. Since r1 is smaller, we use it as the build
relation and r2 as the probe relation. If M > 800/M , i.e. no need for recursive partitioning, then the cost is 3(1500 + 800) = 6900 disk accesses, else
the cost is 2(1500 + 800) logM−1 (800) − 1! + 1500 + 800 disk accesses.
13.6 Design a variant of the hybrid merge – join algorithm for the case where both
relations are not physically sorted, but both have a sorted secondary index on
the join attributes.
Answer: We merge the leaf entries of the first sorted secondary index with
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Query Processing
the leaf entries of the second sorted secondary index. The result file contains
pairs of addresses, the first address in each pair pointing to a tuple in the first
relation, and the second address pointing to a tuple in the second relation.
This result file is first sorted on the first relation’s addresses. The relation
is then scanned in physical storage order, and addresses in the result file are
replaced by the actual tuple values. Then the result file is sorted on the second
relation’s addresses, allowing a scan of the second relation in physical storage
order to complete the join.
13.7 The indexed nested-loop join algorithm described in Section 13.5.3 can be inefficient if the index is a secondary index, and there are multiple tuples with the
same value for the join attributes. Why is it inefficient? Describe a way, using
sorting, to reduce the cost of retrieving tuples of the inner relation. Under what
conditions would this algorithm be more efficient than hybrid merge– join?
Answer: If there are multiple tuples in the inner relation with the same value
for the join attributes, we may have to access that many blocks of the inner
relation for each tuple of the outer relation. That is why it is inefficient. To reduce this cost we can perform a join of the outer relation tuples with just the
secondary index leaf entries, postponing the inner relation tuple retrieval. The
result file obtained is then sorted on the inner relation addresses, allowing an
efficient physical order scan to complete the join.
Hybrid merge–join requires the outer relation to be sorted. The above algorithm does not have this requirement, but for each tuple in the outer relation it
needs to perform an index lookup on the inner relation. If the outer relation is
much larger than the inner relation, this index lookup cost will be less than the
sorting cost, thus this algorithm will be more efficient.
13.8 Estimate the number of block accesses required by your solution to Exercise 13.6 for r1 1 r2 , where r1 and r2 are as defined in Exercise 13.5.
Answer: r1 occupies 800 blocks, and r2 occupies 1500 blocks. Let there be
n pointers per index leaf block (we assume that both the indices have leaf
blocks and pointers of equal sizes). Let us assume M pages of memory, M <
800. r1 ’s index will need B1 = 20000
n ! leaf blocks, and r2 ’s index will need
B2 = 45000
!
leaf
blocks.
Therefore
the merge join will need B3 = B1 + B2
n
accesses, without output. The number of output tuples is estimated as no =
20000∗45000
max(V (C,r1 ),V (C,r2 )) !. Each output tuple will need two pointers, so the number
no
of blocks of join output will be Bo1 = n/2
!. Hence the join needs Bj = B3 +Bo1
disk block accesses.
Now we have to replace the pointers by actual tuples. For the first sorting,
=
Bs1
Bo1 (2 logM−1 (Bo1 /M )! + 2) disk accesses are needed, including the writing
of output to disk. The number of blocks of r1 which have to be accessed in
order to replace the pointers with tuple values is min(800, no). Let n1 pairs of
the form (r1 tuple, pointer to r2 ) fit in one disk block. Therefore the intermediate result after replacing the r1 pointers will occupy Bo2 = (no /n1 )! blocks.
Exercises
159
Hence the first pass of replacing the r1 -pointers will cost Bf = Bs1 + Bo1 +
min(800, no) + Bo2 disk accesses.
The second pass for replacing the r2 -pointers has a similar analysis. Let n2
tuples of the final join fit in one block. Then the second pass of replacing the
r2 -pointers will cost Bs = Bs2 + Bo2 + min(1500, no) disk accesses, where
Bs2 = Bo2 (2 logM−1 (Bo2 /M )! + 2).
Hence the total number of disk accesses for the join is Bj + Bf + Bs , and the
number of pages of output is no /n2 !.
13.9 Let r and s be relations with no indices, and assume that the relations are not
sorted. Assuming infinite memory, what is the lowest cost way (in terms of I/O
operations) to compute r 1 s? What is the amount of memory required for this
algorithm?
Answer: We can store the entire smaller relation in memory, read the larger
relation block by block and perform nested loop join using the larger one as the
outer relation. The number of I/O operations is equal to br + bs , and memory
requirement is min(br , bs ) + 2 pages.
13.10 Suppose that a B+ -tree index on branch-city is available on relation branch, and
that no other index is available. List different ways to handle the following
selections that involve negation?
a. σ¬(branch -city<“Brooklyn”) (branch)
b. σ¬(branch -city=“Brooklyn”) (branch)
c. σ¬(branch -city<“Brooklyn” ∨ assets<5000) (branch)
Answer:
a. Use the index to locate the first tuple whose branch-city field has value
“Brooklyn”. From this tuple, follow the pointer chains till the end, retrieving all the tuples.
b. For this query, the index serves no purpose. We can scan the file sequentially and select all tuples whose branch-city field is anything other than
“Brooklyn”.
c. This query is equivalent to the query
σ(branch-city≥“Brooklyn” ∧ assets<5000) (branch)
Using the branch-city index, we can retrieve all tuples with branch-city value
greater than or equal to “Brooklyn” by following the pointer chains from
the first “Brooklyn” tuple. We also apply the additional criteria of assets <
5000 on every tuple.
13.11 The hash join algorithm as described in Section 13.5.5 computes the natural join
of two relations. Describe how to extend the hash join algorithm to compute
the natural left outer join, the natural right outer join and the natural full outer
join. (Hint: Keep extra information with each tuple in the hash index, to detect
whether any tuple in the probe relation matches the tuple in the hash index.)
Try out your algorithm on the customer and depositor relations.
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Chapter 13
Query Processing
customer-name customer-street
Adams
Spring
Brooks
Senator
Hayes
Main
Johnson
Alma
Jones
Main
Lindsay
Park
Curry
North
Smith
North
Turner
Putnam
Glenn
Sand Hill
Green
Walnut
Williams
Nassau
Figure 13.17
customer-city
Pittsfield
Brooklyn
Harrison
Palo Alto
Harrison
Pittsfield
Rye
Rye
Stamford
Woodside
Stamford
Princeton
Sample customer relation
Answer: For the probe relation tuple tr under consideration, if no matching
tuple is found in the build relation’s hash partition, it is padded with nulls and
included in the result. This will give us the natural left outer join tr 1 ts . To
get the natural right outer join tr 1 ts , we can keep a boolean flag with each
tuple in the current build relation partition Hsi residing in memory, and set it
whenever any probe relation tuple matches with it. When we are finished with
Hsi , all the tuples in it which do not have their flag set, are padded with nulls
and included in the result. To get the natural full outer join, we do both the
above operations together.
To try out our algorithm, we use the sample customer and depositor relations of Figures 13.17 and 13.18. Let us assume that there is enough memory
to hold three tuples of the build relation plus a hash index for those three tuples. We use depositor as the build relation. We use the simple hashing function
which returns the first letter of customer-name. Taking the first partitions, we get
Hr1 = {(“Adams”, “Spring”, “Pittsfield”)}, and Hs1 = φ. The tuple in the
probe relation partition will have no matching tuple, so (“Adams”, “Spring”,
“Pittsfield”, null) is outputted. In the partition for “D”, the lone build relation
tuple is unmatched, thus giving an output tuple (“David”, null, null, A-306).
In the partition for “H”, we find a match for the first time, producing the output tuple (”Hayes”, ”Main”, ”Harrison”, A-102). Proceeding in a similar way,
we process all the partitions and complete the join.
13.12 Write pseudocode for an iterator that implements indexed nested-loop join,
where the outer relation is pipelined. Use the standard iterator functions in
your pseudocode. Show what state information the iterator must maintain between calls.
Answer: Let outer be the iterator which returns successive tuples from the
pipelined outer relation. Let inner be the iterator which returns successive tuples of the inner relation having a given value at the join attributes. The inner
iterator returns these tuples by performing an index lookup. The functions In-
Exercises
161
customer-name account-number
Johnson
A-101
Johnson
A-201
Jones
A-217
Smith
A-215
Hayes
A-102
Turner
A-305
David
A-306
Lindsay
A-222
Figure 13.18
Sample depositor relation
dexedNLJoin::open, IndexedNLJoin::close and IndexedNLJoin::next to implement the indexed nested-loop join iterator are given below. The two iterators outer and inner, the value of the last read outer relation tuple tr and a flag
doner indicating whether the end of the outer relation scan has been reached
are the state information which need to be remembered by IndexedNLJoin
between calls.
IndexedNLJoin::open()
begin
outer.open();
inner.open();
doner := false;
if(outer.next() = false)
move tuple from outer’s output buffer to tr ;
else
doner := true;
end
IndexedNLJoin::close()
begin
outer.close();
inner.close();
end
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Chapter 13
Query Processing
boolean IndexedNLJoin::next()
begin
while(¬doner )
begin
if(inner.next(tr [JoinAttrs]) = false)
begin
move tuple from inner’s output buffer to ts ;
compute tr 1 ts and place it in output buffer;
return true;
end
else
if(outer.next() = false)
begin
move tuple from outer’s output buffer to tr ;
rewind inner to first tuple of s;
end
else
doner := true;
end
return false;
end
13.13 Design sorting based and hashing algorithms for computing the division operation.
Answer: Suppose r(T ∪ S) and s(S) be two relations and r ÷ s has to be computed.
For sorting based algorithm, sort relation s on S. Sort relation r on (T, S).
Now, start scanning r and look at the T attribute values of the first tuple. Scan r
till tuples have same value of T . Also scan s simultaneously and check whether
every tuple of s also occurs as the S attribute of r, in a fashion similar to merge
join. If this is the case, output that value of T and proceed with the next value of
T . Relation s may have to be scanned multiple times but r will only be scanned
once. Total disk accesses, after sorting both the relations, will be |r| + N ∗ |s|,
where N is the number of distinct values of T in r.
We assume that for any value of T , all tuples in r with that T value fit in
memory, and consider the general case at the end. Partition the relation r on
attributes in T such that each partition fits in memory (always possible because
of our assumption). Consider partitions one at a time. Build a hash table on the
tuples, at the same time collecting all distinct T values in a separate hash table.
For each value of T , Now, for each value VT of T , each value s of S, probe the
hash table on (VT , s). If any of the values is absent, discard the value VT , else
output the value VT .
In the case that not all r tuples with one value for T fit in memory, partition r
and s on the S attributes such that the condition is satisfied, run the algorithm
Exercises
163
on each corresponding pair of partitions ri and si . Output the intersection of
the T values generated in each partition.
C H A P T E R
1 4
Query Optimization
This chapter describes how queries are optimized. It starts off with statistics used for
query optimization, and outlines how to use these statistics to estimate selectivities
and query result sizes used for cost estimation. Equivalence rules are covered next,
followed by a description of a query optimization algorithm modeled after the classic
System R optimization algorithm, and coverage of nested subquery optimization.
The chapter ends with a description of materialized views, their role in optimization
and a description of incremental view-maintenance algorithms.
It should be emphasized that the estimates of query sizes and selectivities are approximate, even if the assumptions made, such as uniformity, hold. Further, the cost
estimates for various algorithms presented in Chapter 13 assume only a minimal
amount of memory, and are thus worst case estimates with respect to buffer space
availability. As a result, cost estimates are never very accurate. However, practical
experience has shown that such estimates tend to be reasonably accurate, an plans
optimal with respect to estimated cost are rarely much worse than a truly optimal
plan.
We do not expect students to memorize the size-estimates, and we stress only the
process of arriving at the estimates, not the exact values. Precision in terms of estimated cost is not a worthwhile goal, so estimates off by a few I/O operations can be
considered acceptable.
If a commercial database system is available for student use, a lab assignment
may be designed in which students measure the performance speedup provided by
indices. Many commercial database products have an “explain plan” feature that lets
the user find the evaluation plan used on a query. It is worthwhile asking students to
explore the plans generated for different queries, with and without indices. A more
challenging assignment is to design tests to see how clever the query optimizer is,
and to guess from these experiments which of the optimization techniques covered
in the chapter are used in the system.
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Changes from 3rd edition:
The major change from the previous edition is that the 3rd edition chapter on query
processing has been split into two chapters.
Coverage of size estimation for different operations, which was earlier covered
along with algorithms for the operations has now been separated out into a separate
section (Section 14.2). Some of the formulae for estimation of statistics have been
simplified and a few new ones have been added.
Pseudocode has been provided for the dynamic programming algorithm for join
order optimization. There is a new section on optimization of nested subqueries,
which forms an important part of SQL optimization. The section on materialized
views is also new to this edition.
Exercises
14.1 Clustering indices may allow faster access to data than a nonclustering index
affords. When must we create a nonclustering index, despite the advantages of
a clustering index? Explain your answer.
Answer: There can be only one clustering index for a file, based on the ordering key. Any query which needs to search on the other non-ordering keys will
need the non-clustering index. If the query accesses a majority of the tuples in
the file, it may be more efficient to sort the file on the desired key, rather than
using the non-clustering index.
14.2 Consider the relations r1 (A, B, C), r2 (C, D, E), and r3 (E, F ), with primary keys
A, C, and E, respectively. Assume that r1 has 1000 tuples, r2 has 1500 tuples,
and r3 has 750 tuples. Estimate the size of r1 1 r2 1 r3 , and give an efficient
strategy for computing the join.
Answer:
• The relation resulting from the join of r1 , r2 , and r3 will be the same no
matter which way we join them, due to the associative and commutative
properties of joins. So we will consider the size based on the strategy of
((r1 1 r2 ) 1 r3 ). Joining r1 with r2 will yield a relation of at most 1000
tuples, since C is a key for r2 . Likewise, joining that result with r3 will
yield a relation of at most 1000 tuples because E is a key for r3 . Therefore
the final relation will have at most 1000 tuples.
• An efficient strategy for computing this join would be to create an index
on attribute C for relation r2 and on E for r3 . Then for each tuple in r1 , we
do the following:
a. Use the index for r2 to look up at most one tuple which matches the C
value of r1 .
b. Use the created index on E to look up in r3 at most one tuple which
matches the unique value for E in r2 .
14.3 Consider the relations r1 (A, B, C), r2 (C, D, E), and r3 (E, F ) of Exercise 14.2.
Assume that there are no primary keys, except the entire schema. Let V (C, r1 )
be 900, V (C, r2 ) be 1100, V (E, r2 ) be 50, and V (E, r3 ) be 100. Assume that r1
Exercises
167
has 1000 tuples, r2 has 1500 tuples, and r3 has 750 tuples. Estimate the size of
r1 1 r2 1 r3 , and give an efficient strategy for computing the join.
Answer: The estimated size of the relation can be determined by calculating
the average number of tuples which would be joined with each tuple of the
second relation. In this case, for each tuple in r1 , 1500/V (C, r2 ) = 15/11 tuples (on the average) of r2 would join with it. The intermediate relation would
have 15000/11 tuples. This relation is joined with r3 to yield a result of approximately 10,227 tuples (15000/11 × 750/100 = 10227). A good strategy should
join r1 and r2 first, since the intermediate relation is about the same size as r1
or r2 . Then r3 is joined to this result.
14.4 Suppose that a B+ -tree index on branch-city is available on relation branch, and
that no other index is available. What would be the best way to handle the
following selections that involve negation?
a. σ¬(branch -city<“Brooklyn”) (branch)
b. σ¬(branch -city=“Brooklyn”) (branch)
c. σ¬(branch -city<“Brooklyn” ∨ assets<5000) (branch)
Answer:
a. Use the index to locate the first tuple whose branch-city field has value
“Brooklyn”. From this tuple, follow the pointer chains till the end, retrieving all the tuples.
b. For this query, the index serves no purpose. We can scan the file sequentially and select all tuples whose branch-city field is anything other than
“Brooklyn”.
c. This query is equivalent to the query
σ(branch-city≥“Brooklyn” ∧ assets<5000) (branch)
Using the branch-city index, we can retrieve all tuples with branch-city value
greater than or equal to “Brooklyn” by following the pointer chains from
the first “Brooklyn” tuple. We also apply the additional criteria of assets <
5000 on every tuple.
14.5 Suppose that a B+ -tree index on (branch-name, branch-city) is available on relation branch. What would be the best way to handle the following selection?
σ(branch-city<“Brooklyn”) ∧ (assets<5000)∧(branch-name=“Downtown”) (branch)
Answer: Using the index, we locate the first tuple having branch-name “Downtown”. We then follow the pointers retrieving successive tuples as long as
branch-city is less than “Brooklyn”. From the tuples retrieved, the ones not satisfying the condition (assets < 5000) are rejected.
14.6 Show that the following equivalences hold. Explain how you can apply then
to improve the efficiency of certain queries:
a. E1 1θ (E2 − E3 ) = (E1 1θ E2 − E1 1θ E3 ).
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b. σθ ( A GF (E)) = A GF (σθ (E)), where θ uses only attributes from A.
c. σθ (E1 1 E2 ) = σθ (E1 ) 1 E2 where θ uses only attributes from E1 .
Answer:
1θ (E2 − E3 ) = (E1 1θ E2 − E1 1θ E3 ).
Let us rename (E1 1θ (E2 −E3 )) as R1 , (E1 1θ E2 ) as R2 and (E1 1θ E3 )
as R3 . It is clear that if a tuple t belongs to R1 , it will also belong to R2 . If
a tuple t belongs to R3 , t[E3 ’s attributes] will belong to E3 , hence t cannot
belong to R1 . From these two we can say that
a. E1
∀t, t ∈ R1 ⇒ t ∈ (R2 − R3 )
It is clear that if a tuple t belongs to R2 − R3 , then t[R2 ’s attributes] ∈ E2
and t[R2 ’s attributes] ∈ E3 . Therefore:
∀t, t ∈ (R2 − R3 ) ⇒ t ∈ R1
The above two equations imply the given equivalence.
This equivalence is helpful because evaluation of the right hand side
join will produce many tuples which will finally be removed from the result. The left hand side expression can be evaluated more efficiently.
b. σθ ( A GF (E)) = A GF (σθ (E)), where θ uses only attributes from A.
θ uses only attributes from A. Therefore if any tuple t in the output of
A GF (E) is filtered out by the selection of the left hand side, all the tuples in
E whose value in A is equal to t[A] are filtered out by the selection of the
right hand side. Therefore:
∀t, t ∈ σθ ( A GF (E)) ⇒ t ∈
A GF (σθ (E))
Using similar reasoning, we can also conclude that
∀t, t ∈
A GF (σθ (E))
⇒ t ∈ σθ ( A GF (E))
The above two equations imply the given equivalence.
This equivalence is helpful because evaluation of the right hand side
avoids performing the aggregation on groups which are anyway going to
be removed from the result. Thus the right hand side expression can be
evaluated more efficiently than the left hand side expression.
c. σθ (E1 1 E2 ) = σθ (E1 ) 1 E2 where θ uses only attributes from E1 .
θ uses only attributes from E1 . Therefore if any tuple t in the output of
(E1 1 E2 ) is filtered out by the selection of the left hand side, all the tuples
in E1 whose value is equal to t[E1 ] are filtered out by the selection of the
right hand side. Therefore:
∀t, t ∈ σθ (E1
1 E2 )
⇒ t ∈ σθ (E1 )
1 E2
Using similar reasoning, we can also conclude that
∀t, t ∈ σθ (E1 )
1 E2
⇒ t ∈ σθ (E1
1 E2 )
The above two equations imply the given equivalence.
Exercises
169
This equivalence is helpful because evaluation of the right hand side
avoids producing many output tuples which are anyway going to be removed from the result. Thus the right hand side expression can be evaluated more efficiently than the left hand side expression.
14.7 Show how to derive the following equivalences by a sequence of transformations using the equivalence rules in Section 14.3.1.
a. σθ1 ∧θ2 ∧θ3 (E) = σθ1 (σθ2 (σθ3 (E)))
b. σθ1 ∧θ2 (E1 1θ3 E2 ) = σθ1 (E1 1θ3 (σθ2 (E2 ))), where θ2 involves only attributes from E2
Answer:
a. Using rule 1, σθ1 ∧θ2 ∧θ3 (E) becomes σθ1 (σθ2 ∧θ3 (E)). On applying rule 1
again, we get σθ1 (σθ2 (σθ3 (E))).
b. σθ1 ∧θ2 (E1 1θ3 E2 ) on applying rule 1 becomes σθ1 (σθ2 (E1 1θ3 E2 )). This
on applying rule 7.a becomes σθ1 (E1 1θ3 (σθ2 (E2 ))).
14.8 For each of the following pairs of expressions, give instances of relations that
show the expressions are not equivalent.
a. ΠA (R − S) and ΠA (R) − ΠA (S)
b. σB<4 ( A Gmax (B) (R)) and A Gmax (B) (σB<4 (R))
c. In the preceding expressions, if both occurrences of max were replaced by
min would the expressions be equivalent?
d. (R 1 S) 1 T and R 1 (S 1 T )
In other words, the natural left outer join is not associative.
(Hint: Assume that the schemas of the three relations are R(a, b1), S(a, b2),
and T (a, b3), respectively.)
e. σθ (E1 1 E2 ) and E1 1 σθ (E2 ), where θ uses only attributes from E2
Answer:
a. R = {(1, 2)}, S = {(1, 3)}
The result of the left hand side expression is {(1)}, whereas the result of
the right hand side expression is empty.
b. R = {(1, 2), (1, 5)}
The left hand side expression has an empty result, whereas the right
hand side one has the result {(1, 2)}.
c. Yes, on replacing the max by the min, the expressions will become equivalent. Any tuple that the selection in the rhs eliminates would not pass the
selection on the lhs if it were the minimum value, and would be eliminated
anyway if it were not the minimum value.
d. R = {(1, 2)}, S = {(2, 3)}, T = {(1, 4)}. The left hand expression gives
{(1, 2, null, 4)} whereas the the right hand expression gives {(1, 2, 3, null)}.
e. Let R be of the schema (A, B) and S of (A, C). Let R = {(1, 2)}, S =
{(2, 3)} and let θ be the expression C = 1. The left side expression’s result
is empty, whereas the right side expression results in {(1, 2, null)}.
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14.9 SQL allows relations with duplicates (Chapter 4).
a. Define versions of the basic relational-algebra operations σ, Π, ×, 1, −, ∪,
and ∩ that work on relations with duplicates, in a way consistent with SQL.
b. Check which of the equivalence rules 1 through 7.b hold for the multiset
version of the relational-algebra defined in part a.
Answer:
a. We define the multiset versions of the relational-algebra operators here.
Given multiset relations r1 and r2 ,
i. σ
Let there be c1 copies of tuple t1 in r1 . If t1 satisfies the selection σθ ,
then there are c1 copies of t1 in σθ (r1 ), otherwise there are none.
ii. Π
For each copy of tuple t1 in r1 , there is a copy of tuple ΠA (t1 ) in
ΠA (r1 ), where ΠA (t1 ) denotes the projection of the single tuple t1 .
iii. ×
If there are c1 copies of tuple t1 in r1 and c2 copies of tuple t2 in r2 ,
then there are c1 ∗ c2 copies of the tuple t1 .t2 in r1 × r2 .
iv. 1
The output will be the same as a cross product followed by a selection.
v. −
If there are c1 copies of tuple t in r1 and c2 copies of t in r2 , then there
will be c1 − c2 copies of t in r1 − r2 , provided that c1 − c2 is positive.
vi. ∪
If there are c1 copies of tuple t in r1 and c2 copies of t in r2 , then there
will be c1 + c2 copies of t in r1 ∪ r2 .
vii. ∩
If there are c1 copies of tuple t in r1 and c2 copies of t in r2 , then there
will be min(c1 , c2 ) copies of t in r1 ∩ r2 .
b. All the equivalence rules 1 through 7.b of section 14.3.1 hold for the multiset version of the relational-algebra defined in the first part.
There exist equivalence rules which hold for the ordinary relationalalgebra, but do not hold for the multiset version. For example consider
the rule :A∩B
=
A ∪ B − (A − B) − (B − A)
This is clearly valid in plain relational-algebra. Consider a multiset instance in which a tuple t occurs 4 times in A and 3 times in B. t will occur
3 times in the output of the left hand side expression, but 6 times in the
output of the right hand side expression. The reason for this rule to not
hold in the multiset version is the asymmetry in the semantics of multiset
union and intersection.
14.10 ∗∗Show that, with n relations, there are (2(n− 1))!/(n− 1)! different join orders.
Exercises
171
Hint: A complete binary tree is one where every internal node has exactly
two children. Use the fact that the number of different complete binary trees
.
with n leaf nodes is n1 2(n−1)
(n−1)
If you wish, you can derive the formula for the number of complete binary
trees with n nodes from the formula for the number of binary
trees with n
2n
1
nodes. The number of binary trees with n nodes is n+1
;
this
number is
n
known as the Catalan number, and its derivation can be found in any standard
textbook on data structures or algorithms.
Answer: Each join order is a complete binary tree (every non-leaf node has
exactly two children) with the relations as the leaves. The number of different
(see any standard textbook
complete binary trees with n leaf nodes is n1 2(n−1)
(n−1)
on Discrete Structures, eg. ”Fundamentals of Data Structures” by Horowitz
and Sahni, for a proof). Multiplying this by n! for the number of permutations
of the n leaves, we get the desired result.
14.11 ∗∗Show that the lowest-cost join order can be computed in time O(3n ). Assume
that you can store and look up information about a set of relations (such as the
optimal join order for the set, and the cost of that join order) in constant time. (If
you find this exercise difficult, at least show the looser time bound of O(22n ).)
Answer: Consider the dynamic programming algorithm given in Figure 14.5
in the textbook. For each subset having k + 1 relations, the optimal join order
can be computed in time 2k+1 . That is because for one particular pair of subsets
k+1
A and B, we need constant time and there
−2 different subsets
at most 2
n are
that A can denote. Thus, over all the k+1 subsets of size k + 1, this cost is
n k+1
. Summing over all k from 1 to n − 1 gives the binomial expansion of
k+1 2
((1 + x)n − x) with x = 2. Thus the total cost is less than 3n .
14.12 Show that, if only left-deep join trees are considered, as in the System R optimizer, the time taken to find the most efficient join order is around n2n . Assume
that there is only one interesting sort order.
Answer: The derivation of time taken is similar to the general case, except that
instead of considering 2k+1 − 2 subsets of size less than or equal to k for A, we
only need to consider k + 1 subsets of size exactly equal to k. That is because
the right hand operand of the topmost join has to be a single relation. Therebest
the total cost for finding the
n−1
join order for all subsets of size k + 1 is
fore
n
(k
+
1),
which
is
equal
to
n
k+1
k . Summing over all k from 1 to n− 1 using
n−1
the binomial expansion of (1 + x)
with x = 1, gives a total cost of less than
n2n−1 .
14.13 A set of equivalence rules is said to be complete if, whenever two expressions
are equivalent, one can be derived from the other by a sequence of uses of the
equivalence rules. Is the set of equivalence rules that we considered in Section 14.3.1 complete? Hint: Consider the equivalence σ3=5 (r) = { }.
Answer: Two relational expressions are defined to be equivalent when on all
input relations, they give the same output. The set of equivalence rules con-
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Query Optimization
sidered in Section 14.3.1 is not complete. The expressions σ3=5 (r) and { } are
equivalent, but this cannot be shown by using just these rules.
14.14 Decorrelation:
a. Write a nested query on the relation account to find for each branch with
name starting with “B”, all accounts with the maximum balance at the
branch.
b. Rewrite the preceding query, without using a nested subquery; in other
words, decorrelate the query.
c. Give a procedure (similar that that described in Section 14.4.5) for decorrelating such queries.
Answer:
a. The nested query is as follows:
select S.acount-number
from account S
where S.branch-name like ’B%’ and
S.balance =
(select max(T.balance)
from account T
where T.branch-name = S.branch-name)
b. The decorrelated query is as follows:
create table t1 as
select branch-name, max(balance)
from account
group by branch-name
select account-no
from
account, t1
where account.branch-name like ’B%’ and
account.branch-name = t1 .branch-name and
account.balance = t1 .balance
c. In general, consider the queries of the form:
select · · ·
from L1
where P1 and
A1 op
(select f(A2 )
from L2
where P2 )
Exercises
173
where f is some aggregate function on attributes A2 , and op is some boolean
binary operator. The query can be rewritten as
create table t1 (V, Ag2 ) as
select V, f(A2 )
from L2
where P21
group by V
select · · ·
from
L 1 , t1
where P1 and P22 and
A1 op t1 .Ag2
where
i. V contains all the attributes that are used in the selections involving
correlation variables in the nested query,
ii. predicate P21 contains predicates in P2 without selections involving correlation variables
iii. P22 introduces the selections involving the correlation variables. (If predicates in P22 refer to the relation names in L2 they must be rewritten to
refer to relation t1 .)
14.15 Describe how to incrementally maintain the results of the following operations,
on both insertions and deletions.
a. Union and set difference
b. Left outer join
Answer:
a. Given materialized view v = r ∪ s, when a tuple is inserted in r, we check
if it is present in v, and if not we add it to v. When a tuple is deleted from
r, we check if it is there in s, and if not, we delete it from v. Inserts and
deletes in s are handled in symmetric fashion.
For set difference, given view v = r − s, when a tuple is inserted in r,
we check if it is present in s, and if not we add it to v. When a tuple is
deleted from r, we delete it from v if present. When a tuple is inserted in s,
we delete it from v if present. When a tuple is deleted from s, we check if
it is present in r, and if so we add it to v.
b. Given materialized view v = r 1 s, when a set of tuples ir is inserted
in r, we add the tuples ir 1 s to the view. When ir is deleted from r, we
delete ir 1 s from the view. When a set of tuples is is inserted in s, we
compute r 1 is . We find all the tuples of r which previously did not match
any tuple from s(i.e. those padded with null in r 1 s) but which match is .
We remove all those null padded entries from the view and add the tuples
r 1 s to the view. When is is deleted from s, we delete the tuples r 1 is
from the view. Also we find all the tuples in r which match is but which do
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Query Optimization
not match any other tuples in s. We add all those to the view, after padding
them with null values.
14.16 Give an example of an expression defining a materialized view and two situations (sets of statistics for the input relations and the differentials) such that
incremental view maintenance is better than recomputation in one situation,
and recomputation is better in the other situation.
Answer: Let r, s and t be three relations. Consider a materialized view on
these defined by (r 1 s 1 t). Suppose relation r does not have any attributes
common to s or t, while s and t have foreign key relationship. Each of them
have 1000 tuples and 100 tuples are added to r. Then recomputation is better
because (s 1 t) can be computed first which will have 1000 tuples. It can then
be joined with t. In incremental view maintenance, the increment in t will first
be joined with either s or t which will have 100000 tuples (cartesian product).
This huge relation will then be joined with t which will be very expensive.
However, if 100 tuples are added to s instead of r in the above situation,
incremental view maintenance will obviously be better as increment in s can
be joined with t to get a relation of size 100 which can then be joined with r.
C H A P T E R
1 5
Transactions
This chapter provides an overview of transaction processing. It first motivates the
problems of atomicity, consistency, isolation and durability, and introduces the notion
of ACID transactions. It then presents some naive schemes, and their drawbacks,
thereby motivating the techniques described in Chapters 16 and 17. The rest of the
chapter describes the notion of schedules and the concept of serializability.
We strongly recommend covering this chapter in a first course on databases, since
it introduces concepts that every database student should be aware of. Details on
how to implement the transaction properties are covered in Chapters 16 and 17.
In the initial presentation to the ACID requirements, the isolation requirement
on concurrent transactions does not insist on serializability. Following Haerder and
Reuter [1983], isolation just requires that the events within a transaction must be hidden from other transactions running concurrently, in order to allow rollback. However, later in the chapter, and in most of the book (except in Chapter 24), we use the
stronger condition of serializability as a requirement on concurrent transactions.
Changes from 3rd edition:
Testing of view serializability has been dropped from this chapter (and from the
book), since it does not have any practical significance.
Exercises
15.1 List the ACID properties. Explain the usefulness of each.
Answer: The ACID properties, and the need for each of them are:• Consistency:
Execution of a transaction in isolation (that is, with no other transaction
executing concurrently) preserves the consistency of the database. This is
typically the responsibility of the application programmer who codes the
transactions.
175
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Chapter 15
Transactions
• Atomicity:
Either all operations of the transaction are reflected properly in the database,
or none are. Clearly lack of atomicity will lead to inconsistency in the
database.
• Isolation:
When multiple transactions execute concurrently, it should be the case
that, for every pair of transactions Ti and Tj , it appears to Ti that either
Tj finished execution before Ti started, or Tj started execution after Ti finished. Thus, each transaction is unaware of other transactions executing
concurrently with it. The user view of a transaction system requires the
isolation property, and the property that concurrent schedules take the system from one consistent state to another. These requirements are satisfied
by ensuring that only serializable schedules of individually consistency
preserving transactions are allowed.
• Durability:
After a transaction completes successfully, the changes it has made to
the database persist, even if there are system failures.
15.2 Suppose that there is a database system that never fails. Is a recovery manager
required for this system?
Answer: Even in this case the recovery manager is needed to perform roll-back
of aborted transactions.
15.3 Consider a file system such as the one on your favorite operating system.
a. What are the steps involved in creation and deletion of files, and in writing
data to a file?
b. Explain how the issues of atomicity and durability are relevant to the creation and deletion of files, and to writing data to files.
Answer: There are several steps in the creation of a file. A storage area is
assigned to the file in the file system, a unique i-number is given to the file
and an i-node entry is inserted into the i-list. Deletion of file involves exactly
opposite steps.
For the file system user in UNIX, durability is important for obvious reasons, but atomicity is not relevant generally as the file system doesn’t support
transactions. To the file system implementor though, many of the internal file
system actions need to have transaction semantics. All the steps involved in
creation/deletion of the file must be atomic, otherwise there will be unreferenceable files or unusable areas in the file system.
15.4 Database-system implementers have paid much more attention to the ACID
properties than have file-system implementers. Why might this be the case?
Answer: Database systems usually perform crucial tasks whose effects need to
be atomic and durable, and whose outcome affects the real world in a permanent manner. Examples of such tasks are monetary transactions, seat bookings
etc. Hence the ACID properties have to be ensured. In contrast, most users of
Exercises
177
file systems would not be willing to pay the price (monetary, disk space, time)
of supporting ACID properties.
15.5 During its execution, a transaction passes through several states, until it finally
commits or aborts. List all possible sequences of states through which a transaction may pass. Explain why each state transition may occur.
Answer: The possible sequences of states are:a. active → partially committed → committed. This is the normal sequence a successful transaction will follow. After executing all its statements it enters
the partially committed state. After enough recovery information has been
written to disk, the transaction finally enters the committed state.
b. active → partially committed → aborted. After executing the last statement
of the transaction, it enters the partially committed state. But before enough
recovery information is written to disk, a hardware failure may occur destroying the memory contents. In this case the changes which it made to
the database are undone, and the transaction enters the aborted state.
c. active → failed → aborted. After the transaction starts, if it is discovered at
some point that normal execution cannot continue (either due to internal
program errors or external errors), it enters the failed state. It is then rolled
back, after which it enters the aborted state.
15.6 Justify the following statement: Concurrent execution of transactions is more
important when data must be fetched from (slow) disk or when transactions
are long, and is less important when data is in memory and transactions are
very short.
Answer: If a transaction is very long or when it fetches data from a slow disk,
it takes a long time to complete. In absence of concurrency, other transactions
will have to wait for longer period of time. Average responce time will increase.
Also when the transaction is reading data from disk, CPU is idle. So resources
are not properly utilized. Hence concurrent execution becomes important in
this case. However, when the transactions are short or the data is available in
memory, these problems do not occur.
15.7 Explain the distinction between the terms serial schedule and serializable schedule.
Answer: A schedule in which all the instructions belonging to one single transaction appear together is called a serial schedule. A serializable schedule has a
weaker restriction that it should be equivalent to some serial schedule. There
are two definitions of schedule equivalence – conflict equivalence and view
equivalence. Both of these are described in the chapter.
15.8 Consider the following two transactions:
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Chapter 15
Transactions
T1 : read(A);
read(B);
if A = 0 then B := B + 1;
write(B).
T2 : read(B);
read(A);
if B = 0 then A := A + 1;
write(A).
Let the consistency requirement be A = 0 ∨ B = 0, with A = B = 0 the
initial values.
a. Show that every serial execution involving these two transactions preserves the consistency of the database.
b. Show a concurrent execution of T1 and T2 that produces a nonserializable
schedule.
c. Is there a concurrent execution of T1 and T2 that produces a serializable
schedule?
Answer:
a. There are two possible executions: T1 T2 and T2 T1 .
Case 1:
initially
after T1
after T2
A
0
0
0
B
0
1
1
Consistency met: A = 0 ∨ B = 0 ≡ T ∨ F = T
Case 2:
initially
after T2
after T1
A
0
1
1
B
0
0
0
Consistency met: A = 0 ∨ B = 0 ≡ F ∨ T = T
b. Any interleaving of T1 and T2 results in a non-serializable schedule.
T1
T2
T4
T3
T5
Figure 15.18. Precedence graph.
Exercises
T1
179
T2
read(A)
read(B)
read(A)
read(B)
if A = 0 then B = B + 1
if B = 0 then A = A + 1
write(A)
write(B)
c. There is no parallel execution resulting in a serializable schedule. From
part a. we know that a serializable schedule results in A = 0 ∨ B = 0. Suppose we start with T1 read(A). Then when the schedule ends, no matter
when we run the steps of T2 , B = 1. Now suppose we start executing T2
prior to completion of T1 . Then T2 read(B) will give B a value of 0. So
when T2 completes, A = 1. Thus B = 1 ∧ A = 1 → ¬ (A = 0 ∨ B = 0).
Similarly for starting with T2 read(B).
15.9 Since every conflict-serializable schedule is view serializable, why do we emphasize conflict serializability rather than view serializability?
Answer: Most of the concurrency control protocols (protocols for ensuring
that only serializable schedules are generated) used in practise are based on
conflict serializability—they actually permit only a subset of conflict serializable schedules. The general form of view serializability is very expensive to
test, and only a very restricted form of it is used for concurrency control.
15.10 Consider the precedence graph of Figure 15.18. Is the corresponding schedule
conflict serializable? Explain your answer.
Answer: There is a serializable schedule corresponding to the precedence
graph below, since the graph is acyclic. A possible schedule is obtained by
doing a topological sort, that is, T1 , T2 , T3 , T4 , T5 .
T1
T2
T4
T3
T5
15.11 What is a recoverable schedule? Why is recoverability of schedules desirable?
Are there any circumstances under which it would be desirable to allow nonrecoverable schedules? Explain your answer.
Answer: A recoverable schedule is one where, for each pair of transactions
Ti and Tj such that Tj reads data items previously written by Ti , the commit
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Transactions
operation of Ti appears before the commit operation of Tj . Recoverable schedules are desirable because failure of a transaction might otherwise bring the
system into an irreversibly inconsistent state. Nonrecoverable schedules may
sometimes be needed when updates must be made visible early due to time
constraints, even if they have not yet been committed, which may be required
for very long duration transactions.
15.12 What is a cascadeless schedule? Why is cascadelessness of schedules desirable?
Are there any circumstances under which it would be desirable to allow noncascadeless schedules? Explain your answer.
Answer: A cascadeless schedule is one where, for each pair of transactions
Ti and Tj such that Tj reads data items previously written by Ti , the commit
operation of Ti appears before the read operation of Tj . Cascadeless schedules
are desirable because the failure of a transaction does not lead to the aborting
of any other transaction. Of course this comes at the cost of less concurrency.
If failures occur rarely, so that we can pay the price of cascading aborts for the
increased concurrency, noncascadeless schedules might be desirable.
C H A P T E R
1 6
Concurrency Control
This chapter describes how to control concurrent execution in a database, in order to
ensure the isolation properties of transactions. A variety of protocols are described
for this purpose. If time is short, some of the protocols may be omitted. We recommend covering, at the least, two-phase locking (Sections 16.1.1), through 16.1.3, deadlock detection and recovery (Section 16.6, omitting Section 16.6.1), the phantom phenomenon (Section 16.7.3), and the concepts behind index concurrency control (the
introductory part of Section 16.9). The most widely used techniques would thereby
be covered.
It is worthwhile pointing out how the graph-based locking protocols generalize
simple protocols, such as ordered acquisition of locks, which students may have studied in an operating system course. Although the timestamp protocols by themselves
are not widely used, multiversion two-phase locking (Section 16.5.2) is of increasing importance since it allows long read-only transactions to run concurrently with
updates.
The phantom phenomenon is often misunderstood by students as showing that
two-phase locking is incorrect. It is worth stressing that transactions that scan a relation must read some data to find out what tuples are in the relation; as long as this
data is itself locked in a two-phase manner, the phantom phenomenon will not arise.
Changes from 3rd edition:
This chapter has been reorganized from the previous edition. Some of the material
from the Concurrency Control chapter of the second edition (Chapter 11), such as
schedules and testing for serializability have been moved into Chapter 15 of the third
edition. The sections on deadlock handling (Section 16.6) and concurrency in index
structures (Section 16.9) have been moved in from Chapter 12 of the second edition
(Transaction Processing). The section on multiversion two-phase locking is new.
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Exercises
16.1 Show that the two-phase locking protocol ensures conflict serializability, and
that transactions can be serialized according to their lock points.
Answer:
16.2 Consider the following two transactions:
T31 : read(A);
read(B);
if A = 0 then B := B + 1;
write(B).
T32 : read(B);
read(A);
if B = 0 then A := A + 1;
write(A).
Add lock and unlock instructions to transactions T31 and T32 , so that they observe the two-phase locking protocol. Can the execution of these transactions
result in a deadlock?
Answer:
a. Lock and unlock instructions:
T31 : lock-S(A)
read(A)
lock-X(B)
read(B)
if A = 0
then B := B + 1
write(B)
unlock(A)
unlock(B)
T32 :
lock-S(B)
read(B)
lock-X(A)
read(A)
if B = 0
then A := A + 1
write(A)
unlock(B)
unlock(A)
b. Execution of these transactions can result in deadlock. For example, consider the following partial schedule:
Exercises
T31
lock-S(A)
183
T32
lock-S(B)
read(B)
read(A)
lock-X(B)
lock-X(A)
The transactions are now deadlocked.
16.3 What benefit does strict two-phase locking provide? What disadvantages result?
Answer: Because it produces only cascadeless schedules, recovery is very easy.
But the set of schedules obtainable is a subset of those obtainable from plain
two phase locking, thus concurrency is reduced.
16.4 What benefit does rigorous two-phase locking provide? How does it compare
with other forms of two-phase locking?
Answer: Rigorous two-phase locking has the advantages of strict 2PL. In addition it has the property that for two conflicting transactions, their commit order
is their serializability order. In some systems users might expect this behavior.
16.5 Most implementations of database systems use strict two-phase locking. Suggest three reasons for the popularity of this protocol.
Answer: It is relatively simple to implement, imposes low rollback overhead
because of cascadeless schedules, and usually allows an acceptable level of
concurrency.
16.6 Consider a database organized in the form of a rooted tree. Suppose that we
insert a dummy vertex between each pair of vertices. Show that, if we follow
the tree protocol on the new tree, we get better concurrency than if we follow
the tree protocol on the original tree.
Answer: The proof is in Buckley and Silberschatz, “Concurrency Control in
Graph Protocols by Using Edge Locks,” Proc. ACM SIGACT-SIGMOD Symposium on the Principles of Database Systems, 1984.
16.7 Show by example that there are schedules possible under the tree protocol that
are not possible under the two-phase locking protocol, and vice versa.
Answer: Consider the tree-structured database graph given below.
cA
cB
cC
Schedule possible under tree protocol but not under 2PL:
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T1
lock(A)
lock(B)
unlock(A)
T2
lock(A)
lock(C)
unlock(B)
lock(B)
unlock(A)
unlock(B)
unlock(C)
Schedule possible under 2PL but not under tree protocol:
T1
lock(A)
T2
lock(B)
lock(C)
unlock(B)
unlock(A)
unlock(C)
16.8 Consider the following extension to the tree-locking protocol, which allows
both shared and exclusive locks:
• A transaction can be either a read-only transaction, in which case it can
request only shared locks, or an update transaction, in which case it can
request only exclusive locks.
• Each transaction must follow the rules of the tree protocol. Read-only transactions may lock any data item first, whereas update transactions must
lock the root first.
Show that the protocol ensures serializability and deadlock freedom.
Answer: The proof is in Kedem and Silberschatz, “Locking Protocols: From
Exclusive to Shared Locks,” JACM Vol. 30, 4, 1983.
16.9 Consider the following graph-based locking protocol, which allows only exclusive lock modes, and which operates on data graphs that are in the form of
a rooted directed acyclic graph.
• A transaction can lock any vertex first.
• To lock any other vertex, the transaction must be holding a lock on the
majority of the parents of that vertex.
Show that the protocol ensures serializability and deadlock freedom.
Answer: The proof is in Kedem and Silberschatz, “Controlling Concurrency
Using Locking Protocols,” Proc. Annual IEEE Symposium on Foundations of
Computer Science, 1979.
16.10 Consider the following graph-based locking protocol that allows only exclusive lock modes, and that operates on data graphs that are in the form of a
rooted directed acyclic graph.
Exercises
185
• A transaction can lock any vertex first.
• To lock any other vertex, the transaction must have visited all the parents
of that vertex, and must be holding a lock on one of the parents of the
vertex.
Show that the protocol ensures serializability and deadlock freedom.
Answer: The proof is in Kedem and Silberschatz, “Controlling Concurrency
Using Locking Protocols,” Proc. Annual IEEE Symposium on Foundations of
Computer Science, 1979.
16.11 Consider a variant of the tree protocol called the forest protocol. The database
is organized as a forest of rooted trees. Each transaction Ti must follow the
following rules:
• The first lock in each tree may be on any data item.
• The second, and all subsequent, locks in a tree may be requested only if
the parent of the requested node is currently locked.
• Data items may be unlocked at any time.
• A data item may not be relocked by Ti after it has been unlocked by Ti .
Show that the forest protocol does not ensure serializability.
Answer: Take a system with 2 trees:
n1
n3
n7
n2
n4
n8
n5
n9
n10
n6
n11
n12
We have 2 transactions, T1 and T2 . Consider the following legal schedule:
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T1
lock(n1)
lock(n3)
write(n3)
unlock(n3)
T2
lock(n2)
lock(n5)
write(n5)
unlock(n5)
lock(n5)
read(n5)
unlock(n5)
unlock(n1)
lock(n3)
read(n3)
unlock(n3)
unlock(n2)
This schedule is not serializable.
16.12 Locking is not done explicitly in persistent programming languages. Rather,
objects (or the corresponding pages) must be locked when the objects are accessed. Most modern operating systems allow the user to set access protections
(no access, read, write) on pages, and memory access that violate the access
protections result in a protection violation (see the Unix mprotect command,
for example). Describe how the access-protection mechanism can be used for
page-level locking in a persistent programming language. (Hint: The technique
is similar to that used for hardware swizzling in Section 11.9.4).
Answer: The access protection mechanism can be used to implement page
level locking. Consider reads first. A process is allowed to read a page only after it read-locks the page. This is implemented by using mprotect to initially
turn off read permissions to all pages, for the process. When the process tries
to access an address in a page, a protection violation occurs. The handler associated with protection violation then requests a read lock on the page, and
after the lock is acquired, it uses mprotect to allow read access to the page by
the process, and finally allows the process to continue. Write access is handled
similarly.
16.13 Consider a database system that includes an atomic increment operation, in
addition to the read and write operations. Let V be the value of data item X.
The operation
increment(X) by C
sets the value of X to V + C in an atomic step. The value of X is not available to
the transaction unless the latter executes a read(X). Figure 16.23 shows a lockcompatibility matrix for three lock modes: share mode, exclusive mode, and
incrementation mode.
Exercises
S
X
I
S
true
false
false
X
false
false
false
187
I
false
false
true
Figure 16.23. Lock-compatibility matrix.
a. Show that, if all transactions lock the data that they access in the corresponding mode, then two-phase locking ensures serializability.
b. Show that the inclusion of increment mode locks allows for increased concurrency. (Hint: Consider check-clearing transactions in our bank example.)
Answer: The proof is in Korth, “Locking Primitives in a Database System,”
JACM Vol. 30, 1983.
16.14 In timestamp ordering, W-timestamp(Q) denotes the largest timestamp of any
transaction that executed write(Q) successfully. Suppose that, instead, we defined it to be the timestamp of the most recent transaction to execute write(Q)
successfully. Would this change in wording make any difference? Explain your
answer.
Answer: It would make no difference. The write protocol is such that the most
recent transaction to write an item is also the one with the largest timestamp to
have done so.
16.15 When a transaction is rolled back under timestamp ordering, it is assigned a
new timestamp. Why can it not simply keep its old timestamp?
Answer: A transaction is rolled back because a newer transaction has read or
written the data which it was supposed to write. If the rolled back transaction
is re-introduced with the same timestamp, the same reason for rollback is still
valid, and the transaction will have be rolled back again. This will continue
indefinitely.
16.16 In multiple-granularity locking, what is the difference between implicit and
explicit locking?
Answer: When a transaction explicitly locks a node in shared or exclusive
mode, it implicitly locks all the descendents of that node in the same mode.
The transaction need not explicitly lock the descendent nodes. There is no difference in the functionalities of these locks, the only difference is in the way
they are acquired, and their presence tested.
16.17 Although SIX mode is useful in multiple-granularity locking, an exclusive and
intend-shared (XIS) mode is of no use. Why is it useless?
Answer: An exclusive lock is incompatible with any other lock kind. Once a
node is locked in exclusive mode, none of the descendents can be simultaneously accessed by any other transaction in any mode. Therefore an exclusive
and intend-shared declaration has no meaning.
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16.18 Use of multiple-granularity locking may require more or fewer locks than an
equivalent system with a single lock granularity. Provide examples of both situations, and compare the relative amount of concurrency allowed.
Answer: If a transaction needs to access a large a set of items, multiple granularity locking requires fewer locks, whereas if only one item needs to be accessed, the single lock granularity system allows this with just one lock. Because all the desired data items are locked and unlocked together in the multiple granularity scheme, the locking overhead is low, but concurrency is also
reduced.
16.19 Consider the validation-based concurrency-control scheme of Section 16.3.
Show that by choosing Validation(Ti ), rather than Start(Ti), as the timestamp of
transaction Ti , we can expect better response time provided that conflict rates
among transactions are indeed low.
Answer: In the concurrency control scheme of Section 16.3 choosing Start(Ti )
as the timestamp of Ti gives a subset of the schedules allowed by choosing
Validation(Ti) as the timestamp. Using Start(Ti ) means that whoever started
first must finish first. Clearly transactions could enter the validation phase
in the same order in which they began executing, but this is overly restrictive. Since choosing Validation(Ti) causes fewer nonconflicting transactions to
restart, it gives the better response times.
16.20 Show that there are schedules that are possible under the two-phase locking
protocol, but are not possible under the timestamp protocol, and vice versa.
Answer: A schedule which is allowed in the two-phase locking protocol but
not in the timestamp protocol is:
T0
T1
Precedence remarks
step
1
lock-S(A)
2
read(A)
3
lock-X(B)
4
write(B)
5
unlock(B)
6
lock-S(B)
7
read(B)
T1 → T0
8
unlock(A)
9
unlock(B)
This schedule is not allowed in the timestamp protocol because at step 7, the
W-timestamp of B is 1.
A schedule which is allowed in the timestamp protocol but not in the twophase locking protocol is:
T0
T1
T2
step
1
write(A)
2
write(A)
3
write(A)
4
write(B)
5
write(B)
Exercises
189
This schedule cannot have lock instructions added to make it legal under
two-phase locking protocol because T1 must unlock (A) between steps 2 and 3,
and must lock (B) between steps 4 and 5.
16.21 For each of the following protocols, describe aspects of practical applications
that would lead you to suggest using the protocol, and aspects that would
suggest not using the protocol:
•
•
•
•
•
•
•
Two-phase locking
Two-phase locking with multiple-granularity locking
The tree protocol
Timestamp ordering
Validation
Multiversion timestamp ordering
Multiversion two-phase locking
Answer:
• Two-phase locking: Use for simple applications where a single granularity
is acceptable. If there are large read-only transactions, multiversion protocols would do better. Also, if deadlocks must be avoided at all costs, the
tree protocol would be preferable.
• Two-phase locking with multiple granularity locking: Use for an application mix where some applications access individual records and others
access whole relations or substantial parts thereof. The drawbacks of 2PL
mentioned above also apply to this one.
• The tree protocol: Use if all applications tend to access data items in an order consistent with a particular partial order. This protocol is free of deadlocks, but transactions will often have to lock unwanted nodes in order to
access the desired nodes.
• Timestamp ordering: Use if the application demands a concurrent execution that is equivalent to a particular serial ordering (say, the order of arrival), rather than any serial ordering. But conflicts are handled by roll-back
of transactions rather than waiting, and schedules are not recoverable. To
make them recoverable, additional overheads and increased response time
have to be tolerated. Not suitable if there are long read-only transactions,
since they will starve. Deadlocks are absent.
• Validation: If the probability that two concurrently executing transactions
conflict is low, this protocol can be used advantageously to get better concurrency and good response times with low overheads. Not suitable under
high contention, when a lot of wasted work will be done.
• Multiversion timestamp ordering: Use if timestamp ordering is appropriate but it is desirable for read requests to never wait. Shares the other disadvantages of the timestamp ordering protocol.
• Multiversion two-phase locking: This protocol allows read-only transactions to always commit without ever waiting. Update transactions follow
2PL, thus allowing recoverable schedules with conflicts solved by waiting
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rather than roll-back. But the problem of deadlocks comes back, though
read-only transactions cannot get involved in them. Keeping multiple versions adds space and time overheads though, therefore plain 2PL may be
preferable in low conflict situations.
16.22 Under a modified version of the timestamp protocol, we require that a commit
bit be tested to see whether a read request must wait. Explain how the commit bit can prevent cascading abort. Why is this test not necessary for write
requests?
Answer: Using the commit bit, a read request is made to wait if the transaction which wrote the data item has not yet committed. Therefore, if the writing
transaction fails before commit, we can abort that transaction alone. The waiting read will then access the earlier version in case of a multiversion system,
or the restored value of the data item after abort in case of a single-version system. For writes, this commit bit checking is unnecessary. That is because either
the write is a “blind” write and thus independent of the old value of the data
item or there was a prior read, in which case the test was already applied.
16.23 Explain why the following technique for transaction execution may provide
better performance than just using strict two-phase locking: First execute the
transaction without acquiring any locks and without performing any writes to
the database as in the validation based techniques, but unlike in the validation
techniques do not perform either validation or perform writes on the database.
Instead, rerun the transaction using strict two-phase locking. (Hint: Consider
waits for disk I/O.)
Answer: TO BE SOLVED
16.24 Under what conditions is it less expensive to avoid deadlock than to allow
deadlocks to occur and then to detect them?
Answer: Deadlock avoidance is preferable if the consequences of abort are
serious (as in interactive transactions), and if there is high contention and a
resulting high probability of deadlock.
16.25 If deadlock is avoided by deadlock avoidance schemes, is starvation still possible? Explain your answer.
Answer: A transaction may become the victim of deadlock-prevention rollback arbitrarily many times, thus creating a potential starvation situation.
16.26 Consider the timestamp ordering protocol, and two transactions, one that
writes two data items p and q, and another that reads the same two data items.
Give a schedule whereby the timestamp test for a write operation fails and
causes the first transaction to be restarted, in turn causing a cascading abort of
the other transaction. Show how this could result in starvation of both transactions. (Such a situation, where two or more processes carry out actions, but are
unable to complete their task because of interaction with the other processes,
is called a livelock.)
Answer: TO BE SOLVED
Exercises
191
16.27 Explain the phantom phenomenon. Why may this phenomenon lead to an incorrect concurrent execution despite the use of the two-phase locking protocol?
Answer: The phantom phenomenon arises when, due to an insertion or deletion, two transactions logically conflict despite not locking any data items in
common. The insertion case is described in the book. Deletion can also lead
to this phenomenon. Suppose Ti deletes a tuple from a relation while Tj scans
the relation. If Ti deletes the tuple and then Tj reads the relation, Ti should be
serialized before Tj . Yet there is no tuple that both Ti and Tj conflict on.
An interpretation of 2PL as just locking the accessed tuples in a relation is
incorrect. There is also an index or a relation data that has information about
the tuples in the relation. This information is read by any transaction that scans
the relation, and modified by transactions that update, or insert into, or delete
from the relation. Hence locking must also be performed on the index or relation data, and this will avoid the phantom phenomenon.
16.28 Devise a timestamp-based protocol that avoids the phantom phenomenon.
Answer: In the text, we considered two approaches to dealing with the phantom phenomenon by means of locking. The coarser granularity approach obviously works for timestamps as well. The B + -tree index based approach can be
adapted to timestamping by treating index buckets as data items with timestamps associated with them, and requiring that all read accesses use an index.
We now show that this simple method works. Suppose a transaction Ti wants
to access all tuples with a particular range of search-key values, using a B + tree index on that search-key. Ti will need to read all the buckets in that index
which have key values in that range. It can be seen that any delete or insert of
a tuple with a key-value in the same range will need to write one of the index
buckets read by Ti . Thus the logical conflict is converted to a conflict on an
index bucket, and the phantom phenomenon is avoided.
16.29 Explain the reason for the use of degree-two consistency. What disadvantages
does this approach have?
Answer: TO BE SOLVED
16.30 Suppose that we use the tree protocol of Section 16.1.5 to manage concurrent
access to a B+ -tree. Since a split may occur on an insert that affects the root, it
appears that an insert operation cannot release any locks until it has completed
the entire operation. Under what circumstances is it possible to release a lock
earlier?
Answer: Note: The tree-protocol of Section 16.1.5 which is referred to in this
question, is different from the multigranularity protocol of Section 16.4 and the
B + -tree concurrency protocol of Section 16.9.
One strategy for early lock releasing is given here. Going down the tree from
the root, if the currently visited node’s child is not full, release locks held on
all nodes except the current node, request an X-lock on the child node, after
getting it release the lock on the current node, and then descend to the child.
On the other hand, if the child is full, retain all locks held, request an X-lock on
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the child, and descend to it after getting the lock. On reaching the leaf node,
start the insertion procedure. This strategy results in holding locks only on the
full index tree nodes from the leaf upwards, uptil and including the first nonfull node.
An optimization to the above strategy is possible. Even if the current node’s
child is full, we can still release the locks on all nodes but the current one. But
after getting the X-lock on the child node, we split it right away. Releasing the
lock on the current node and retaining just the lock on the appropriate split
child, we descend into it making it the current node. With this optimization, at
any time at most two locks are held, of a parent and a child node.
16.31 Give example schedules to show that if any of lookup, insert or delete do not
lock the next key value, the phantom phenomemon could go undetected.
Answer: TO BE SOLVED
C H A P T E R
1 7
Recovery System
This chapter covers failure models and a variety of failure recovery techniques. Recovery in a real-life database systems supporting concurrent transactions is rather
complicated. To help the student understand concepts better, the chapter presents recovery models in increasing degree of complexity. The chapter starts with a simple
model for recovery, ignoring the issue of concurrency. Later, the model is extended to
handle concurrent transactions with strict two-phase locking. Towards the end of the
chapter, we present an “advanced” recovery algorithm that supports early release
of some kinds of locks to improve concurrency, for example in index structures. Finally, we outline the ARIES algorithm variants of which are widely used in practise.
ARIES includes the features of the advanced recovery algorithm, along with several
optimizations that speed up recovery greatly.
We recommed that at least sections up to and including Log-Based Recovery (Section 17.4) be covered. Shadow paging (Section 17.5) is not used very widely, but
is useful for pedagogical reasons, to show alternatives exist to log-based recovery.
Recovery with concurrent transactions (Section 17.6) is an interesting section, and
should be covered along with Buffer Management (Section 17.7), if possible. Section 17.9, covering the advanced recovery algorithm and ARIES, should be omitted
from all except advanced courses. However, it can be used as independent-study
material for well-prepared students even in an introductory course.
There are some points worth noting:
• While reading Section 17.2.2 (Stable storage implementation), it should be recalled from the the discussion in section 11.2.1 that a partial disk block write
can be detected with a high probability using checksums.
• In section 17.4.3, even though the model assumed is one where transactions
execute serially, the recovery procedure says that for all transactions Tk in T
that have no record in the log, execute undo(Tk ). More than
one such transaction can exist, because of successive transaction failures.
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Changes from 3rd edition:
The main changes are (a) we now cover the ARIES recovery algorithm (Section 17.9.6),
and and (b) the section on remote backup systems (Section 17.10) has been moved
into this chapter from its earlier position in Chapter 20. The latter change is motivated by the increasing need for high availability, which will be reflected in a greatly
increased use of remote backup system. Providing high availability can also be considered a job of the recovery system since the same logs can be used for both tasks.
Exercises
17.1 Explain the difference between the three storage types—volatile, nonvolatile,
and stable—in terms of I/O cost.
Answer: Volatile storage is storage which fails when there is a power failure. Cache, main memory, and registers are examples of volatile storage. Nonvolatile storage is storage which retains its content despite power failures. An
example is magnetic disk. Stable storage is storage which theoretically survives
any kind of failure (short of a complete disaster!). This type of storage can only
be approximated by replicating data.
In terms of I/O cost, volatile memory is the fastest and non-volatile storage is typically several times slower. Stable storage is slower than non-volatile
storage because of the cost of data replication.
17.2 Stable storage cannot be implemented.
a. Explain why it cannot be.
b. Explain how database systems deal with this problem.
Answer:
a. Stable storage cannot really be implemented because all storage devices
are made of hardware, and all hardware is vulnerable to mechanical or
electronic device failures.
b. Database systems approximate stable storage by writing data to multiple
storage devices simultaneously. Even if one of the devices crashes, the data
will still be available on a different device. Thus data loss becomes extremely unlikely.
17.3 Compare the deferred- and immediate-modification versions of the log-based
recovery scheme in terms of ease of implementation and overhead cost.
Answer:
• The recovery scheme using a log with deferred updates has the following
advantages over the recovery scheme with immediate updates:
a. The scheme is easier and simpler to implement since fewer operations
and routines are needed, i.e., no UNDO.
b. The scheme requires less overhead since no extra I/O operations need
to be done until commit time (log records can be kept in memory the
entire time).
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c. Since the old values of data do not have to be present in the log-records,
this scheme requires less log storage space.
• The disadvantages of the deferred modification scheme are :
a. When a data item needs to accessed, the transaction can no longer directly read the correct page from the database buffer, because a previous write by the same transaction to the same data item may not have
been propagated to the database yet. It might have updated a local
copy of the data item and deferred the actual database modification.
Therefore finding the correct version of a data item becomes more expensive.
b. This scheme allows less concurrency than the recovery scheme with
immediate updates. This is because write-locks are held by transactions
till commit time.
c. For long transaction with many updates, the memory space occupied
by log records and local copies of data items may become too high.
17.4 Assume that immediate modification is used in a system. Show, by an example,
how an inconsistent database state could result if log records for a transaction
are not output to stable storage prior to data updated by the transaction being
written to disk.
Answer: Consider a banking scheme and a transaction which transfers $50
from account A to account B. The transaction has the following steps:
a.
b.
c.
d.
e.
f.
read(A,a1)
a1 := a1 − 50
write(A,a1)
read(B,b1)
b1 := b1 + 50
write(B,b1)
Suppose the system crashes after the transaction commits, but before its log
records are flushed to stable storage. Further assume that at the time of the
crash the update of A in the third step alone had actually been propagated to
disk whereas the buffer page containing B was not yet written to disk. When
the system comes up it is in an inconsistent state, but recovery is not possible
because there are no log records corresponding to this trabsaction in stable
storage.
17.5 Explain the purpose of the checkpoint mechanism. How often should checkpoints be performed? How does the frequency of checkpoints affect
• System performance when no failure occurs
• The time it takes to recover from a system crash
• The time it takes to recover from a disk crash
Answer: Checkpointing is done with log-based recovery schemes to reduce
the time required for recovery after a crash. If there is no checkpointing, then
the entire log must be searched after a crash, and all transactions undone/redone
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from the log. If checkpointing had been performed, then most of the log-records
prior to the checkpoint can be ignored at the time of recovery.
Another reason to perform checkpoints is to clear log-records from stable
storage as it gets full.
Since checkpoints cause some loss in performance while they are being taken,
their frequency should be reduced if fast recovery is not critical. If we need fast
recovery checkpointing frequency should be increased. If the amount of stable
storage available is less, frequent checkpointing is unavoidable. Checkpoints
have no effect on recovery from a disk crash; archival dumps are the equivalent of checkpoints for recovery from disk crashes.
17.6 When the system recovers from a crash (see Section 17.6.4), it constructs an
undo-list and a redo-list. Explain why log records for transactions on the undolist must be processed in reverse order, while those log records for transactions
on the redo-list are processed in a forward direction.
Answer: The first phase of recovery is to undo the changes done by the failed
transactions, so that all data items which have been modified by them get back
the values they had before the first of the failed transactions started. If several of
the failed transactions had modified the same data item, forward processing of
log-records for undo-list transactions would make the data item get the value
which it had before the last failed transaction to modify that data item started.
This is clearly wrong, and we can see that reverse prcessing gets us the desired
result.
The second phase of recovery is to redo the changes done by committed
transactons, so that all data items which have been modified by them are restored to the value they had after the last of the committed transactions finished. It can be seen that only forward processing of log-records belonging to
redo-list transactions can guarantee this.
17.7 Compare the shadow-paging recovery scheme with the log-based recovery
schemes in terms of ease of implementation and overhead cost.
Answer: The shadow-paging scheme is easy to implement for single-transaction
systems, but difficult for multiple-transaction systems. In particular it is very
hard to allow multiple updates concurrently on the same page. Shadow paging could suffer from extra space overhead, but garbage collection can take
care of that. The I/O overhead for shadow paging is typically higher than the
log based schemes, since the log based schemes need to write one record per
update to the log, whereas the shadow paging scheme needs to write one block
per updated block.
17.8 Consider a database consisting of 10 consecutive disk blocks (block 1, block
2, . . ., block 10). Show the buffer state and a possible physical ordering of the
blocks after the following updates, assuming that shadow paging is used, that
the buffer in main memory can hold only three blocks, and that a least recently
used (LRU) strategy is used for buffer management.
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read block 3
read block 7
read block 5
read block 3
read block 1
modify block 1
read block 10
modify block 5
Answer: The initial ordering of the disk blocks is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Assume that the two blocks following block 10 on the disk, are the first two
blocks in the list of free blocks.
a. The first 3 read steps result in blocks 3, 7, 5 being placed in the buffer.
b. The 4th read step requires no disk access.
c. The 5th read step requires block 1 to be read. Block 7 is the least recently
used block in the buffer, so it is replaced by block 1.
d. The 6th step is to modify block 1. The first free block is removed from the
free block list, and the entry 1 in the current page table is made to point to
it. Block 1 in the buffer is modified. When dirty blocks are flushed back to
disk at the time of transaction commit, they should be written to the disk
blocks pointed to the updated current page table.
e. The 7th step causes block 10 to be read. Block 5 is overwritten in the buffer
since it is the least recently used.
f. In the 8th step, block 3 is replaced by block 5, and then block 5 is modified
as in the 6th step.
Therefore the final disk ordering of blocks is: 2, 3, 4, 6, 7, 8, 9, 10, 1, 5. The set of
blocks in the buffer are: 5 (modified), 10, 1 (modified). These must be flushed
to the respective disk blocks as pointed to by the current page table, before the
transaction performs commit processing.
17.9 Explain how the buffer manager may cause the database to become inconsistent if some log records pertaining to a block are not output to stable storage
before the block is output to disk.
Answer: If a data item x is modified on disk by a transaction before the corresponding log record is written to stable storage, then the only record of the
old value of x is in main memory where it would be lost in a crash. If the
transaction had not yet finished at the time of the crash, an unrecoverable inconsistency will result.
17.10 Explain the benefits of logical logging. Give examples of one situation where
logical logging is preferable to physical logging and one situation where physical logging is preferable to logical logging.
Answer: Logical logging has less log space requirement, and with logical undo
logging it allows early release of locks. This is desirable in situations like concurrency control for index structures, where a very high degree of concurrency
is required. An advantage of employing physical redo logging is that fuzzy
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checkpoints are possible. Thus in a system which needs to perform frequent
checkpoints, this reduces checkpointing overhead.
17.11 Explain the reasons why recovery of interactive transactions is more difficult
to deal with than is recovery of batch transactions. Is there a simple way to deal
with this difficulty? (Hint: Consider an automatic teller machine transaction in
which cash is withdrawn.)
Answer: Interactive transactions are more difficult to recover from than batch
transactions because some actions may be irrevocable. For example, an output
(write) statement may have fired a missile, or caused a bank machine to give
money to a customer. The best way to deal with this is to try to do all output
statements at the end of the transaction. That way if the transaction aborts in
the middle, no harm will be have been done.
17.12 Sometimes a transaction has to be undone after it has commited, because it was
erroneously executed, for example because of erroneous input by a bank teller.
a. Give an example to show that using the normal transaction undo mechanism to undo such a transaction could lead to an inconsistent state.
b. One way to handle this situation is to bring the whole database to a state
prior to the commit of the erroneous transaction (called point-in-time recovery). Transactions that committed later have their effects rolled back with
this scheme.
Suggest a modification to the advanced recovery mechanism to implement point-in-time recovery.
c. Later non-erroneous transactions can be reexecuted logically, but cannot
be reexecuted using their log records. Why?
Answer:
• Consider the a bank account A with balance $100. Consider two transactions T1 and T2 each depositing $10 in the account. Thus the balance would
be $120 after both these transactions are executed. Let the transactions execute in sequence: T1 first and then T2 . The log records corresponding to
the updates of A by transactions T1 and T2 would be < T1 , A, 100, 110 >
and < T2 , A, 110, 120 > resp.
Say, we wish to undo transaction T1 . The normal transaction undo mechanism will replaces the value in question – A in this example – by the oldvalue field in the log record. Thus if we undo transaction T1 using the normal transaction undo mechanism the resulting balance would be $100 and
we would, in effect, undo both transactions, whereas we intend to undo
only transaction T1 .
• ... TO BE FILLED IN ...
• Consider again an example from the first item. Let us assume that both
transactions are undone and the balance is reverted back to the original
value $100.
Now we wish to redo transaction T2 . If we redo the log record < T2 , A, 110, 120 >
corresponding to transaction T2 the balance would become $120 and we
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would, in effect, redo both transactions, whereas we intend to redo only
transaction T2 .
17.13 Logging of updates is not done explicitly in persistent programming languages.
Describe how page access protections provided by modern operating systems
can be used to create before and after images of pages that are updated. (Hint:
See Exercise 16.12.)
Answer: This is implemented by using mprotect to initially turn off access
to all pages, for the process. When the process tries to access an address in a
page, a protection violation occurs. The handler accociated with protection violation then requests a write lock on the page, and after the lock is acquired,
it writes the initial contents (before-image) of the page to the log. It then uses
mprotect to allow write access to the page by the process, and finally allows
the process to continue. When the transaction is ready to commit, and before it
releases the lock on the page, it writes the contents of the page (after-image) to
the log. These before- and after- images can be used for recovery after a crash.
This scheme can be optimized to not write the whole page to log for undo
logging, provided the program pins the page in memory.
17.14 ARIES assumes there is space in each page for an LSN. When dealing with large
objects that span multiple pages, such as operating system files, an entire page
may be used by an object, leaving no space for the LSN. Suggest a technique to
handle such a situation; your technique must support physical redos but need
not support physiological redos.
Answer: TO BE FILLED IN. Separate array.
17.15 Explain the difference between a system crash and a “disaster.”
Answer: In a system crash, the CPU goes down, and disk may also crash. But
stable-storage at the site is assumed to survive system crashes. In a “disaster”,
everything at a site is destroyed. Stable storage needs to be distributed to survive disasters.
17.16 For each of the following requirements, identify the best choice of degree of
durability in a remote backup system:
a. Data loss must be avoided but some loss of availability may be tolerated.
b. Transaction commit must be accomplished quickly, even at the cost of loss
of some committed transactions in a disaster.
c. A high degree of availability and durability is required, but a longer running time for the transaction commit protocol is acceptable.
Answer:
a. Two very safe is suitable here because it guarantees durability of updates
by committed transactions, though it can proceed only if both primary and
backup sites are up. Availability is low, but it is mentioned that this is acceptable.
b. One safe committing is fast as it does not have to wait for the logs to reach
the backup site. Since data loss can be tolerated, this is the best option.
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c. With two safe committing, the probability of data loss is quite low, and
also commits can proceed as long as at least the primary site is up. Thus
availability is high. Commits take more time than in the one safe protocol,
but that is mentioned as acceptable.
C H A P T E R
1 8
Database System Architectures
The chapter is suitable for an introductory course. We recommend covering it, at
least as self-study material, since students are quite likely to use the non-centralized
(particularly client-server) database architectures when they enter the real world. The
material in this chapter could potentially be supplemented by the two-phase commit
protocol (2PC), (Section 19.4.1 from Chapter 19) to give students an overview of the
most important details of non-centralized database architectures.
Changes from 3rd edition:
Coverage of database process structures (Section 18.2.1) is new in this edition. Coverage of network technology has been updated, and storage area networks are briefly
covered.
Exercises
18.1 Why is it relatively easy to port a database from a single processor machine to
a multiprocessor machine if individual queries need not be parallelized?
Answer: Porting is relatively easy to a shared memory multiprocessor machine. Databases designed for single-processor machines already provide multitasking, allowing multiple processes to run on the same processor in a timeshared manner, giving a view to the user of multiple processes running in parallel. Thus, coarse-granularity parallel machines logically appear to be identical to single-processor machines, making the porting relatively easy.
Porting a database to a shared disk or shared nothing multiprocessor architecture is a little harder.
18.2 Transaction server architectures are popular for client-server relational databases, where transactions are short. On the other hand, data server architectures are popular for client-server object-oriented database systems, where transactions are expected to be relatively long. Give two reasons why data servers
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may be popular for object-oriented databases but not for relational databases.
Answer: Data servers are good if data transfer is small with respect to computation, which is often the case in applications of OODBs such as computer
aided design. In contrast, in typical relational database applications such as
transaction processing, a transaction performs little computation but may touch
several pages, which will result in a lot of data transfer with little benefit in a
data server architecture. Another reason is that structures such as indices are
heavily used in relational databases, and will become spots of contention in
a data server architecture, requiring frequent data transfer. There are no such
points of frequent contention in typical current-day OODB applications such
as computer aided design.
18.3 Instead of storing shared structures in shared memory, an alternative architecture would be to store them in the local memory of a special process, and access
the shared data by interprocess communication with the process. What would
be the drawback of such an architecture?
Answer: The drawbacks would be that two interprocess messages would be
required to acquire locks, one for the request and one to confirm grant. Interprocess communication is much more expensive than memory access, so the
cost of locking would increase. The process storing the shared structures could
also become a bottleneck.
The benefit of this alternative is that the lock table is protected better from
erroneous updates since only one process can access it.
18.4 In typical client– server systems the server machine is much more powerful
than the clients; that is, its processor is faster, it may have multiple processors, and it has more memory and disk capacity. Consider instead a scenario
where client and server machines have exactly the same power. Would it make
sense to build a client– server system in such a scenario? Why? Which scenario
would be better suited to a data-server architecture?
Answer: With powerful clients, it still makes sense to have a client-server
system, rather than a fully centralized system. If the data-server architecture
is used, the powerful clients can off-load all the long and compute intensive
transaction processing work from the server, freeing it to perform only the
work of satisfying read-write requests. even if the transaction-server model
is used, the clients still take care of the user-interface work, which is typically
very compute-intensive.
A fully distributed system might seem attractive in the presence of powerful clients, but client-server systems still have the advantage of simpler concurrency control and recovery schemes to be implemented on the server alone,
instead of having these actions distributed in all the machines.
18.5 Consider an object-oriented database system based on a client-server architecture, with the server acting as a data server.
a. What is the effect of the speed of the interconnection between the client
and the server on the choice between object and page shipping?
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203
b. If page shipping is used, the cache of data at the client can be organized
either as an object cache or a page cache. The page cache stores data in units
of a page, while the object cache stores data in units of objects. Assume
objects are smaller than a page. Describe one benefit of an object cache
over a page cache.
Answer:
a. We assume that objects are smaller than a page and fit in a page. If the interconnection link is slow it is better to choose object shipping, as in page
shipping a lot of time will be wasted in shipping objects that might never
be needed. With a fast interconnection though, the communication overheads and latencies, not the actual volume of data to be shipped, becomes
the bottle neck. In this scenario page shipping would be preferable.
b. Two benefits of an having an object-cache rather than a page-cache, even if
page shipping is used, are:i. When a client runs out of cache space, it can replace objects without
replacing entire pages. The reduced caching granularity might result
in better cache-hit ratios.
ii. It is possible for the server to ask clients to return some of the locks
which they hold, but don’t need (lock de-escalation). Thus there is
scope for greater concurrency. If page caching is used, this is not possible.
18.6 What is lock de-escalation, and under what conditions is it required? Why is it
not required if the unit of data shipping is an item?
Answer: In a client-server system with page shipping, when a client requests
an item, the server typically grants a lock not on the requested item, but on the
page having the item, thus implicitly granting locks on all the items in the page.
The other items in the page are said to be prefetched. If some other client subsequently requests one of the prefetched items, the server may ask the owner
of the page lock to transfer back the lock on this item. If the page lock owner
doesn’t need this item, it de-escalates the page lock that it holds, to item locks
on all the items that it is actually accessing, and then returns the locks on the
unwanted items. The server can then grant the latter lock request.
If the unit of data shipping is an item, there are no coarser granularity locks;
even if prefetching is used, it is typically implemented by granting individual
locks on each of the prefetched items. Thus when the server asks for a return of
a lock, there is no question of de-escalation, the requested lock is just returned
if the client has no use for it.
18.7 Suppose you were in charge of the database operations of a company whose
main job is to process transactions. Suppose the company is growing rapidly
each year, and has outgrown its current computer system. When you are choosing a new parallel computer, what measure is most relevant—speedup, batch
scaleup, or transaction scaleup? Why?
Answer: With increasing scale of operations, we expect that the number of
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transactions submitted per unit time increases. On the other hand, we wouldn’t
expect most of the individual transactions to grow longer, nor would we require that a given transaction should execute more quickly now than it did before. Hence transaction scale-up is the most relevant measure in this scenario.
18.8 Suppose a transaction is written in C with embedded SQL, and about 80 percent
of the time is spent in the SQL code, with the remaining 20 percent spent in C
code. How much speedup can one hope to attain if parallelism is used only for
the SQL code? Explain.
Answer: Since the part which cannot be parallelized takes 20% of the total
running time, the best speedup we can hope for has to be less than 5.
18.9 What are the factors that can work against linear scaleup in a transaction processing system? Which of the factors are likely to be the most important in each
of the following architectures: shared memory, shared disk, and shared nothing?
Answer: Increasing contention for shared resources prevents linear scale-up
with increasing parallelism. In a shared memory system, contention for memory (which implies bus contention) will result in falling scale-up with increasing parallelism. In a shared disk system, it is contention for disk and bus access
which affects scale-up. In a shared-nothing system, inter-process communication overheads will be the main impeding factor. Since there is no shared memory, acquiring locks, and other activities requiring message passing between
processes will take more time with increased parallelism.
18.10 Consider a bank that has a collection of sites, each running a database system.
Suppose the only way the databases interact is by electronic transfer of money
between one another. Would such a system qualify as a distributed database?
Why?
Answer: In a distributed system, all the sites typically run the same database
management software, and they share a global schema. Each site provides an
environment for execution of both global transactions initiated at remote sites
and local transactions. The system described in the question does not have
these properties, and hence it cannot qualify as a distributed database.
18.11 Consider a network based on dial-up phone lines, where sites communicate
periodically, such as every night. Such networks are often configured with a
server site and multiple client sites. The client sites connect only to the server,
and exchange data with other clients by storing data at the server and retrieving data stored at the server by other clients. What is the advantage of such an
architecture over one where a site can exchange data with another site only by
first dialing it up?
Answer: With the central server, each site does not have to remember which
site to contact when a particular data item is to be requested. The central server
alone needs to remember this, so data items can be moved around easily, depending on which sites access which items most frequently. Other house-keeping
tasks are also centralized rather than distributed, making the system easier to
develop and maintain. Of course there is the disadvantage of a total shutdown
Exercises
205
in case the server becomes unavailable. Even if it is running, it may become a
bottleneck because every request has to be routed via it.
C H A P T E R
1 9
Distributed Databases
Distributed databases in general, and heterogeneous distributed databases in particular, are of increasing practical importance, as organizations attempt to integrate
databases across physical and organizational boundaries. Such interconnection of
databases to create a distributed or multidatabase is in fact proving crucial to competitiveness for many companies. This chapter reconsiders the issues addressed earlier
in the text, such as query processing, recovery and concurrency control, from the
standpoint of distributed databases.
This is a long chapter, and is appropriate only for an advanced course. Single topics may be chosen for inclusion in an introductory course. Good choices include distributed data storage, heterogeneity and two-phase commit.
Changes from 3rd edition:
This chapter has changed significantly from the previous edition.
• The emphasis on transparency in the earlier edition has been dropped, and
instead the chapter begins by considering the distinction between heterogeneous and homogeneous distributed databases.
• All details of three phase commit have been dropped since it is not widely
used in practise.
• We have introduced coverage of alternative models of transaction processing
in Section 19.4.3, with emphasis on the persistent messaging based approach
to distributed transactions.
• Replication with weak levels of consistency, which is widely used in practise,
is now covered in Section 19.5.3.
• Distributed algorithms for deadlock detection has been dropped since they
are too complicated and expensive to be practical.
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• We have introduced detailed coverage of failure handing for providing high
availability in distributed databases (Section 19.6).
• Heterogeneous databases are now covered in more detail in Section 19.8, while
details of weak levels of serializability in multidatabases have been moved to
Chapter 24.
• Coverage of directory systems, with emphasis on LDAP, has been introduced
in this edition (Section 19.9).
Exercises
19.1 Discuss the relative advantages of centralized and distributed databases.
Answer:
• A distributed database allows a user convenient and transparent access to
data which is not stored at the site, while allowing each site control over
its own local data. A distributed database can be made more reliable than
a centralized system because if one site fails, the database can continue
functioning, but if the centralized system fails, the database can no longer
continue with its normal operation. Also, a distributed database allows
parallel execution of queries and possibly splitting one query into many
parts to increase throughput.
• A centralized system is easier to design and implement. A centralized system is cheaper to operate because messages do not have to be sent.
19.2 Explain how the following differ: fragmentation transparency, replication
transparency, and location transparency.
Answer:
a. With fragmentation transparency, the user of the system is unaware of any
fragmentation the system has implemented. A user may formulate queries
against global relations and the system will perform the necessary transformation to generate correct output.
b. With replication transparency, the user is unaware of any replicated data.
The system must prevent inconsistent operations on the data. This requires
more complex concurrency control algorithms.
c. Location transparency means the user is unaware of where data are stored.
The system must route data requests to the appropriate sites.
19.3 How might a distributed database designed for a local-area network differ
from one designed for a wide-area network?
Answer: Data transfer on a local-area network (LAN) is much faster than on
a wide-area network (WAN). Thus replication and fragmentation will not increase throughput and speed-up on a LAN, as much as in a WAN. But even in
a LAN, replication has its uses in increasing reliability and availability.
19.4 When is it useful to have replication or fragmentation of data? Explain your
answer.
Answer: Replication is useful when there are many read-only transactions at
Exercises
209
different sites wanting access to the same data. They can all execute quickly
in parallel, accessing local data. But updates become difficult with replication.
Fragmentation is useful if transactions on different sites tend to access different
parts of the database.
19.5 Explain the notions of transparency and autonomy. Why are these notions desirable from a human-factors standpoint?
Answer: Autonomy is the amount of control a single site has over the local
database. It is important because users at that site want quick and correct access to local data items. This is especially true when one considers that local
data will be most frequently accessed in a database. Transparency hides the
distributed nature of the database. This is important because users should not
be required to know about location, replication, fragmentation or other implementation aspects of the database.
19.6 To build a highly available distributed system, you must know what kinds of
failures can occur.
a. List possible types of failure in a distributed system.
b. Which items in your list from part a are also applicable to a centralized
system?
Answer:
a. The types of failure that can occur in a distributed system include
i. Computer failure (site failure).
ii. Disk failure.
iii. Communication failure.
b. The first two failure types can also occur on centralized systems.
19.7 Consider a failure that occurs during 2PC for a transaction. For each possible
failure that you listed in Exercise 19.6a, explain how 2PC ensures transaction
atomicity despite the failure.
Answer: A proof that 2PC guarantees atomic commits/aborts inspite of site
and link failures, follows. The main idea is that after all sites reply with a
message, only the co-ordinator of a transaction can make a commit or abort decision. Any subsequent commit or abort by a site can happen
only after it ascertains the co-ordinator’s decision, either directly from the coordinator, or indirectly from some other site. Let us enumerate the cases for a
site aborting, and then for a site committing.
a. A site can abort a transaction T (by writing an log record) only
under the following circumstances:i. It has not yet written a log-record. In this case, the coordinator could not have got, and will not get a or message from this site. Therefore only an abort decision can be
made by the co-ordinator.
ii. It has written the log record, but on inquiry it found out
that some other site has an log record. In this case it is
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correct for it to abort, because that other site would have ascertained
the co-ordinator’s decision (either directly or indirectly) before actually aborting.
iii. It is itself the co-ordinator. In this case also no site could have committed, or will commit in the future, because commit decisions can be
made only by the co-ordinator.
b. A site can commit a transaction T (by writing an log record)
only under the following circumstances:i. It has written the log record, and on inquiry it found out
that some other site has a log record. In this case it is
correct for it to commit, because that other site would have ascertained
the co-ordinator’s decision (either directly or indirectly) before actually
committing.
ii. It is itself the co-ordinator. In this case no other participating site can
abort/ would have aborted, because abort decisions are made only by
the co-ordinator.
19.8 Consider a distributed system with two sites, A and B. Can site A distinguish
among the following?
• B goes down.
• The link between A and B goes down.
• B is extremely overloaded and response time is 100 times longer than normal.
What implications does your answer have for recovery in distributed systems?
Answer: Site A cannot distinguish between the three cases until communication has resumed with site B. The action which it performs while B is inaccessible must be correct irrespective of which of these situations has actually
occurred, and must be such that B can re-integrate consistently into the distributed system once communication is restored.
19.9 The persistent messaging scheme described in this chapter depends on timestamps combined with discarding of received messages if they are too old.
Suggest an alternative scheme based on sequence numbers instead of timestamps.
Answer: We can have a scheme based on sequence numbers similar to the
scheme based on timestamps. We tag each message with a sequence number
that is unique for the (sending site, receiving site) pair. The number is increased
by 1 for each new message sent from the sending site to the receiving site.
The receiving site stores and acknowledges a received message only if it
has received all lower numbered messages also; the message is stored in the
received-messages relation.
The sending site retransmits a message until it has received an ack from the
receiving site containing the sequence number of the transmitted message, or
a higher sequence number. Once the acknowledgment is received, it can delete
the message from its send queue.
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211
The receiving site discards all messages it receives that have a lower sequence number than the latest stored message from the sending site. The receiving site discards from received-messages all but the (number of the) most
recent message from each sending site (message can be discarded only after
being processed locally).
Note that this scheme requires a fixed (and small) overhead at the receiving site for each sending site, regardless of the number of messages received.
In contrast the timestamp scheme requires extra space for every message. The
timestamp scheme would have lower storage overhead if the number of messages received within the timeout interval is small compared to the number
of sites, whereas the sequence number scheme would have lower overhead
otherwise.
19.10 Give an example where the read one, write all available approach leads to an
erroneous state.
Answer: Consider the balance in an account, replicated at N sites. Let the current balance be $100 – consistent across all sites. Consider two transactions T1
and T2 each depositing $10 in the account. Thus the balance would be $120
after both these transactions are executed. Let the transactions execute in sequence: T1 first and then T2 . Let one of the sites, say s, be down when T1 is
executed and transaction t2 reads the balance from site s. One can see that the
balance at the primary site would be $110 at the end.
19.11 If we apply a distributed version of the multiple-granularity protocol of Chapter 16 to a distributed database, the site responsible for the root of the DAG may
become a bottleneck. Suppose we modify that protocol as follows:
• Only intention-mode locks are allowed on the root.
• All transactions are given all possible intention-mode locks on the root
automatically.
Show that these modifications alleviate this problem without allowing any
nonserializable schedules.
Answer: Serializability is assured since we have not changed the rules for the
multiple granularity protocol. Since transactions are automatically granted all
intention locks on the root node, and are not given other kinds of locks on it,
there is no need to send any lock requests to the root. Thus the bottleneck is
relieved.
19.12 Explain the difference between data replication in a distributed system and the
maintenance of a remote backup site.
Answer: In remote backup systems all transactions are performed at the primary site and the data is replicated at the remote backup site. The remote
backup site is kept synchronized with the updates at the primary site by sending all log records. Whenever the primary site fails, the remote backup site
takes over processing.
The distributed systems offer greater availability by having multiple copies
of the data at different sites whereas the remote backup systems offer lesser
availability at lower cost and execution overhead.
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In a distributed system, transaction code runs at all the sites whereas in a
remote backup system it runs only at the primary site. The distributed system transactions follow two-phase commit to have the data in consistent state
whereas a remote backup system does not follow two-phase commit and avoids
related overhead.
19.13 Give an example where lazy replication can lead to an inconsistent database
state even when updates get an exclusive lock on the primary (master) copy.
Answer: Consider the balance in an account, replicated at N sites. Let the current balance be $100 – consistent across all sites. Consider two transactions T1
and T2 each depositing $10 in the account. Thus the balance would be $120
after both these transactions are executed. Let the transactions execute in sequence: T1 first and then T2 . Suppose the copy of the balance at one of the
sites, say s, is not consistent – due to lazy replication strategy – with the primary copy after transaction T1 is executed and let transaction T2 read this copy
of the balance. One can see that the balance at the primary site would be $110
at the end.
19.14 Study and summarize the facilities that the database system you are using provides for dealing with inconsistent states that can be reached with lazy propagation of updates.
Answer: TO BE FILLED IN.
19.15 Discuss the advantages and disadvantages of the two methods that we presented in Section 19.5.2 for generating globally unique timestamps.
Answer: The centralized approach has the problem of a possible bottleneck at
the central site and the problem of electing a new central site if it goes down.
The distributed approach has the problem that many messages must be exchanges to keep the system fair, or one site can get ahead of all other sites and
dominate the database.
19.16 Consider the following deadlock-detection algorithm. When transaction Ti , at
site S1 , requests a resource from Tj , at site S3 , a request message with timestamp n is sent. The edge (Ti , Tj , n) is inserted in the local wait-for of S1 . The
edge (Ti , Tj , n) is inserted in the local wait-for graph of S3 only if Tj has received the request message and cannot immediately grant the requested resource. A request from Ti to Tj in the same site is handled in the usual manner;
no timestamps are associated with the edge (Ti , Tj ). A central coordinator invokes the detection algorithm by sending an initiating message to each site in
the system.
On receiving this message, a site sends its local wait-for graph to the coordinator. Note that such a graph contains all the local information that the site has
about the state of the real graph. The wait-for graph reflects an instantaneous
state of the site, but it is not synchronized with respect to any other site.
When the controller has received a reply from each site, it constructs a graph
as follows:
• The graph contains a vertex for every transaction in the system.
Exercises
213
• The graph has an edge (Ti , Tj ) if and only if
There is an edge (Ti , Tj ) in one of the wait-for graphs.
An edge (Ti , Tj , n) (for some n) appears in more than one wait-for
graph.
Show that, if there is a cycle in the constructed graph, then the system is in
a deadlock state, and that, if there is no cycle in the constructed graph, then
the system was not in a deadlock state when the execution of the algorithm
began.
Answer: Let us say a cycle Ti → Tj → · · · → Tm → Ti exists in the graph
built by the controller. The edges in the graph will either be local edges of the
from (Tk , Tl ) or distributed edges of the form (Tk , Tl , n). Each local edge (Tk , Tl )
definitely implies that Tk is waiting for Tl . Since a distributed edge (Tk , Tl , n)
is inserted into the graph only if Tk ’s request has reached Tl and Tl cannot
immediately release the lock, Tk is indeed waiting for Tl . Therefore every edge
in the cycle indeed represents a transaction waiting for another. For a detailed
proof that this imlies a deadlock refer to Stuart et al. [1984].
We now prove the converse implication. As soon as it is discovered that Tk
is waiting for Tl :a. a local edge (Tk , Tl ) is added if both are on the same site.
b. The edge (Tk , Tl , n) is added in both the sites, if Tk and Tl are on different
sites.
Therefore, if the algorithm were able to collect all the local wait-for graphs at
the same instant, it would definitely discover a cycle in the constructed graph,
in case there is a circular wait at that instant. If there is a circular wait at the
instant when the algorithm began execution, none of the edges participating in
that cycle can disappear until the algorithm finishes. Therefore, even though
the algorithm cannot collect all the local graphs at the same instant, any cycle
which existed just before it started will anyway be detected.
19.17 Consider a relation that is fragmented horizontally by plant-number:
employee (name, address, salary, plant-number)
Assume that each fragment has two replicas: one stored at the New York site
and one stored locally at the plant site. Describe a good processing strategy for
the following queries entered at the San Jose site.
a. Find all employees at the Boca plant.
b. Find the average salary of all employees.
c. Find the highest-paid employee at each of the following sites: Toronto, Edmonton, Vancouver, Montreal.
d. Find the lowest-paid employee in the company.
Answer:
a.
i. Send the query Πname (employee) to the Boca plant.
ii. Have the Boca location send back the answer.
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Distributed Databases
i. Compute average at New York.
ii. Send answer to San Jose.
c. i. Send the query to find the highest salaried employee to Toronto, Edmonton, Vancouver, and Montreal.
ii. Compute the queries at those sites.
iii. Return answers to San Jose.
d. i. Send the query to find the lowest salaried employee to New York.
ii. Compute the query at New York.
iii. Send answer to San Jose.
b.
19.18 Consider the relations
employee (name, address, salary, plant-number)
machine (machine-number, type, plant-number)
Assume that the employee relation is fragmented horizontally by plant-number,
and that each fragment is stored locally at its corresponding plant site. Assume
that the machine relation is stored in its entirety at the Armonk site. Describe a
good strategy for processing each of the following queries.
a. Find all employees at the plant that contains machine number 1130.
b. Find all employees at plants that contain machines whose type is “milling
machine.”
c. Find all machines at the Almaden plant.
d. Find employee 1 machine.
Answer:
i. Perform Πplant-number (σmachine-number=1130 (machine)) at Armonk.
ii. Send the query Πname (employee) to all site(s) which are in the result
of the previous query.
iii. Those sites compute the answers.
iv. Union the answers at the destination site.
b. This strategy is the same as 0.a, except the first step should be to perform
a.
Πplant-number (σtype=“milling machine” (machine)) at Armonk.
i. Perform σplant-number = x (machine) at Armonk, where x is the plantnumber for Almaden.
ii. Send the answers to the destination site.
d. Strategy 1:
i. Group machine at Armonk by plant number.
ii. Send the groups to the sites with the corresponding plant-number.
iii. Perform a local join between the local data and the received data.
iv. Union the results at the destination site.
Strategy 2:
Send the machine relation at Armonk, and all the fragments of the
employee relation to the destination site. Then perform the join at the
destination site.
c.
Exercises
215
There is parallelism in the join computation according to the first strategy but not in the second. Nevertheless, in a WAN the amount of data
to be shipped is the main cost factor. We expect that each plant will have
more than one machine, hence the result of the local join at each site will
be a cross-product of the employee tuples and machines at that plant. This
cross-product’s size is greater than the size of the emplyee fragment at that
site. As a result the second strategy will result in less data shipping, and
will be more efficient.
19.19 For each of the strategies of Exercise 19.18, state how your choice of a strategy
depends on:
a. The site at which the query was entered
b. The site at which the result is desired
Answer:
a. Assuming that the cost of shipping the query itself is minimal, the site
at which the query was submitted does not affect our strategy for query
evaluation.
b. For the first query, we find out the plant numbers where the machine number 1130 is present, at Armonk. Then the employee tuples at all those plants
are shipped to the destination site. We can see that this strategy is more or
less independent of the destination site. The same can be said of the second query. For the third query, the selection is performed at Armonk and
results shipped to the destination site. This stratgy is obviously independent of the destination site.
For the fourth query, we have two strategies. The first one performs
local joins at all the plant sites and their results are unioned at the destination site. In the second strategy, the machine relation at Armonk as well
as all the fragments of the employee relation are first shipped to the destination, where the join operation is performed. There is no obvious way to
optimize these two strategies based on the destination site. In the answer
to Exercise 19.18 we saw the reason why the second strategy is expected
to result in less data shipping than the first. That reason is independent of
destination site, and hence we can in general prefer strategy two to strategy one, regardless of the destination site.
19.20 Compute r s for the relations of Figure 19.1.
Answer: The result is as follows.
r s = A B C
1 2 3
5 3 2
19.21 Is ri rj necessarily equal to rj ri ? Under what conditions does ri
rj = rj ri hold?
rj ri . This can be easily seen from
Answer: In general, ri rj =
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Chapter 19
Distributed Databases
TC1
TCn
transaction
coordinator
TM1
TMn
transaction
manager
computer 1
computer n
Figure 19.1
Relations for Exercise 19.20.
Exercise 19.20, in which r s = s r. r s was given in 19.20,
while
s r =
C
3
3
2
D E
4 5
6 8
3 2
By definition, ri rj = ΠRi (ri 1 rj ) and rj ri = ΠRj (ri 1 rj ), where
Ri and Rj are the schemas of ri and rj respectively. For ΠRi (ri 1 rj ) to be
always equal to ΠRj (ri 1 rj ), the schemas Ri and Rj must be the same.
19.22 Given that the LDAP functionality can be implemented on top of a database
system, what is the need for the LDAP standard?
Answer: The reasons are:
a. Directory access protocols are simplified protocols that cater to a limited
type of access to data.
b. Directory systems provide a simple mechanism to name objects in a hierarchical fashion which can be used in a distributed directory system to
specify what information is stored in each of the directory servers. The directory system can be set up to automatically forward queries made at one
site to the other site, without user intervention.
19.23 Describe how LDAP can be used to provide multiple hierarchical views of data,
without replicating the base level data.
Answer: This can be done using referrals. For example an organization may
maintain its information about departments either by geography (i.e. all departments in a site of the the organization) or by structure (i.e. information
about a department from all sites). These two hierarchies can be maintained
by defining two different schemas with department information at a site as
the base information. The entries in the two hierarchies will refer to the base
information entry using referrals.
C H A P T E R
2 0
Parallel Databases
This chapter is suitable for an advanced course, but can also be used for independent
study projects by students of a first course. The chapter covers several aspects of the
design of parallel database systems — partitioning of data, parallelization of individual relational operations, and parallelization of relational expressions. The chapter also briefly covers some systems issues, such as cache coherency and failure resiliency.
The most important applications of parallel databases today are for warehousing and analyzing large amounts of data. Therefore partitioning of data and parallel query processing are covered in significant detail. Query optimization is also of
importance, for the same reason. However, parallel query optimization is still not a
fully solved problem; exhaustive search, as is used for sequential query optimization,
is too expensive in a parallel system, forcing the use of heuristics. Thus parallel query
optimization is an area of ongoing research.
The description of parallel query processing algorithms is based on the sharednothing model. Students may be asked to study how the algorithms can be improved
if shared-memory machines are used instead.
Changes from 3rd edition:
There are no major changes from the previous edition.
Exercises
20.1 For each of the three partitioning techniques, namely round-robin, hash partitioning, and range partitioning, give an example of a query for which that
partitioning technique would provide the fastest response.
Answer:
Round robin partitioning:
When relations are large and queries read entire relations, round-robin
gives good speed-up and fast response time.
217
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Chapter 20
Parallel Databases
Hash partitioning
For point queries, this gives the fastest response, as each disk can process a query simultaneously. If the hash partitioning is uniform, even entire
relation scans can be performed efficiently.
Range partitioning
For range queries which access a few tuples, this gives fast response.
20.2 In a range selection on a range-partitioned attribute, it is possible that only
one disk may need to be accessed. Describe the benefits and drawbacks of this
property.
Answer: If there are few tuples in the queried range, then each query can be
processed quickly on a single disk. This allows parallel execution of queries
with reduced overhead of initiating queries on multiple disks.
On the other hand, if there are many tuples in the queried range, each query
takes a long time to execute as there is no parallelism within its execution. Also,
some of the disks can become hot-spots, further increasing response time.
Hybrid range partitioning, in which small ranges (a few blocks each) are
partitioned in a round-robin fashion, provides the benefits of range partitioning without its drawbacks.
20.3 What factors could result in skew when a relation is partitioned on one of its
attributes by:
a. Hash partitioning
b. Range partitioning
In each case, what can be done to reduce the skew?
Answer:
a. Hash-partitioning:
Too many records with the same value for the hashing attribute, or a
poorly chosen hash function without the properties of randomness and
uniformity, can result in a skewed partition. To improve the situation, we
should experiment with better hashing functions for that relation.
b. Range-partitioning:
Non-uniform distribution of values for the partitioning attribute (including duplicate values for the partitioning attribute) which are not taken
into account by a bad partitioning vector is the main reason for skewed
partitions. Sorting the relation on the partitioning attribute and then dividing it into n ranges with equal number of tuples per range will give a
good partitioning vector with very low skew.
20.4 What form of parallelism (interquery, interoperation, or intraoperation) is likely
to be the most important for each of the following tasks.
a. Increasing the throughput of a system with many small queries
b. Increasing the throughput of a system with a few large queries, when the
number of disks and processors is large
Answer:
Exercises
219
a. When there are many small queries, inter-query parallelism gives good
throughput. Parallelizing each of these small queries would increase the
initiation overhead, without any significant reduction in response time.
b. With a few large queries, intra-query parallelism is essential to get fast response times. Given that there are large number of processors and disks,
only intra-operation parallelism can take advantage of the parallel hardware – for queries typically have few operations, but each one needs to
process a large number of tuples.
20.5 With pipelined parallelism, it is often a good idea to perform several operations
in a pipeline on a single processor, even when many processors are available.
a. Explain why.
b. Would the arguments you advanced in part a hold if the machine has a
shared-memory architecture? Explain why or why not.
c. Would the arguments in part a hold with independent parallelism? (That
is, are there cases where, even if the operations are not pipelined and there
are many processors available, it is still a good idea to perform several
operations on the same processor?)
Answer:
a. The speed-up obtained by parallelizing the operations would be offset by
the data transfer overhead, as each tuple produced by an operator would
have to be transferred to its consumer, which is running on a different processor.
b. In a shared-memory architecture, transferring the tuples is very efficient.
So the above argument does not hold to any significant degree.
c. Even if two operations are independent, it may be that they both supply
their outputs to a common third operator. In that case, running all three on
the same processor may be better than transferring tuples across processors.
20.6 Give an example of a join that is not a simple equi-join for which partitioned
parallelism can be used. What attributes should be used for partitioning?
Answer: We give two examples of such joins.
a. r
1(r.A=s.B)∧(r.A (select max(balance)
from account)
and 1.5∗ balance <= (select max(balance)
from account)
)
union
(select 3, count(∗)
from account
where 1.5∗ balance > (select max(balance)
from account)
)
22.8 Consider the sales relation from Section 22.2. Write an SQL query to compute
the cube operation on the relation, giving the relation in Figure 22.2. Do not
use the with cube construct.
Answer:
Exercises
235
(select color, size, sum(number)
from sales
groupby color, size
)
union
(select color, ’all’, sum(number)
from sales
groupby color
)
union
(select ’all’, size, sum(number)
from sales
groupby size
)
union
(select ’all’, ’all’, sum(number)
from sales
)
22.9 Construct a decision tree classifier with binary splits at each node, using tuples in relation r(A, B, C) shown below as training data; attribute C denotes
the class. Show the final tree, and with each node show the best split for each
attribute along with its information gain value.
(1, 2, a), (2, 1, a), (2, 5, b), (3, 3, b), (3, 6, b), (4, 5, b), (5, 5, c), (6, 3, b), (6, 7, c)
Answer:
22.10 Suppose there are two classification rules, one that says that people with salaries
between $10,000 and $20,000 have a credit rating of good, and another that says
that people with salaries between $20,000 and $30,000 have a credit rating of
good. Under what conditions can the rules be replaced, without any loss of information, by a single rule that says people with salaries between $10,000 and
$30,000 have a credit rating of good.
Answer: Consider the following pair of rules and their confidence levels :
No.
1.
2.
Rule
∀ persons P, 10000 < P.salary ≤ 20000 ⇒
P.credit = good
∀ persons P, 20000 < P.salary ≤ 30000 ⇒
P.credit = good
Conf.
60%
90%
The new rule has to be assigned a confidence-level which is between the
confidence-levels for rules 1 and 2. Replacing the original rules by the new
rule will result in a loss of confidence-level information for classifying persons,
since we cannot distinguish the confidence levels of perople earning between
10000 and 20000 from those of people earning between 20000 and 30000. There-
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Advanced Querying and Information Retrieval
fore we can combine the two rules without loss of information only if their
confidences are the same.
22.11 Suppose half of all the transactions in a clothes shop purchase jeans, and one
third of all transactions in the shop purchase T-shirts. Suppose also that half
of the transactions that purchase jeans also purchase T-shirts. Write down all
the (nontrivial) association rules you can deduce from the above information,
giving support and confidence of each rule.
Answer: The rules are as follows. The last rule can be deduced from the previous ones.
Rule
∀ transactions
∀ transactions
∀ transactions
∀ transactions
T,
T,
T,
T,
Support Conf.
true ⇒ buys(T, jeans)
50%
50%
true ⇒ buys(T, t-shirts)
33%
33%
buys(T, jeans) ⇒ buys(T, t-shirts)
25%
50%
buys(T, t-shirts) ⇒ buys(T, jeans)
25%
75%
22.12 Consider the problem of finding large itemsets.
a. Describe how to find the support for a given collection of itemsets by using
a single scan of the data. Assume that the itemsets and associated information, such as counts, will fit in memory.
b. Suppose an itemset has support less than j. Show that no superset of this
itemset can have support greater than or equal to j.
Answer:
a. Let {S1 , S2 , . . . , Sn } be the collection of item-sets for which we want to find
the support. Associate a counter count(Si ) with each item-set Si .
Initialize each counter to zero. Now examine the transactions one-byone. Let S(T ) be the item-set for a transaction T . For each item-set Si that
is a subset of S(T ), increment the corresponding counter count(Si ).
When all the transactions have been scanned, the values of count(Si ) for
each i will give the support for item-set Si .
b. Let A be an item-set. Consider any item-set B which is a superset of A.
Let τA and τB be the sets of transactions that purchase all items in A and
all items in B, respectively. For example, suppose A is {a, b, c}, and B is
{a, b, c, d}.
A transaction that purchases all items from B must also have purchased
all items from A (since A ⊆ B). Thus, every transaction in τB is also in τA .
This implies that the number of transactions in τB is at most the number of
transactions in τA . In other words, the support for B is at most the support
for A.
Thus, if any item-set has support less than j, all supersets of this item-set
have support less than j.
22.13 Describe benefits and drawbacks of a source-driven architecture for gathering
of data at a data-warehouse, as compared to a destination-driven architecture.
Exercises
237
Answer: In a destination-driven architecture for gathering data, data transfers
from the data sources to the data-warehouse are based on demand from the
warehouse, whereas in a source-driven architecture, the transfers are initiated
by each source.
The benefits of a source-driven architecture are
• Data can be propagated to the destination as soon as it becomes available.
For a destination-driven architecture to collect data as soon as it is available, the warehouse would have to probe the sources frequently, leading
to a high overhead.
• The source does not have to keep historical information. As soon as data
is updated, the source can send an update message to the destination and
forget the history of the updates. In contrast, in a destination-driven architecture, each source has to maintain a history of data which have not yet
been collected by the data warehouse. Thus storage requirements at the
source are lower for a source-driven architecture.
On the other hand, a destination-driven architecture has the following advantages.
• In a source-driven architecture, the source has to be active and must handle error conditions such as not being able to contact the warehouse for
some time. It is easier to implement passive sources, and a single active
warehouse. In a destination-driven architecure, each source is required to
provide only a basic functionality of executing queries.
• The warehouse has more control on when to carry out data gathering activities, and when to process user queries; it is not a good idea to perform
both simultaneously, since they may conflict on locks.
22.14 Consider the schema depicted in Figure 22.9. Give an SQL:1999 query to summarize sales numbers and price by store and date, along with the hierarchies
on store and date.
Answer:
select store-id, city, state, country,
date, month, quarter, year,
sum(number), sum(price)
from sales, store, date
where sales.store-id = store.store-id and
sales.date = date.date
groupby rollup(country, state, city, store-id),
rollup(year, quarter, month, date)
22.15 Compute the relevance (using appropriate definitions of term frequency and
inverse document frequency) of each of the questions in this chapter to the
query “SQL relation.”
Answer: We do not consider the questions containing neither of the keywords
as their relevance to the keywords is zero. The number of words in a question
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Chapter 22
Advanced Querying and Information Retrieval
include stop words. We use the equations given in Section 22.5.1.1 to compute
relevance; the log term in the equation is assumed to be to the base 2.
Q.# #
#
#
“SQL”
“relation” “SQL” “relation”
words “SQL” “relation” term freq. term freq. relv.
relv.
1 84
1
1
0.0170
0.0170
0.0002 0.0002
4 22
0
1
0.0000
0.0641
0.0000 0.0029
5 46
1
1
0.0310
0.0310
0.0006 0.0006
6 22
1
0
0.0641
0.0000
0.0029 0.0000
7 33
1
1
0.0430
0.0430
0.0013 0.0013
8 32
1
3
0.0443
0.1292
0.0013 0.0040
9 77
0
1
0.0000
0.0186
0.0000 0.0002
14 30
1
0
0.0473
0.0000
0.0015 0.0000
15 26
1
1
0.0544
0.0544
0.0020 0.0020
22.16 What is the difference between a false positive and a false drop? If it is essential
that no relevant information be missed by an information retrieval query, is it
acceptable to have either false positives or false drops? Why?
Answer: Information-retrieval systems locate documents that contain a specified keyword by using an index that maps this keyword onto a set of identifiers for documents containing it. Each keyword may be contained in a large
number of documents. To save on storage space for the document identifiers
corresponding to a keyword, the index is sometimes stored such that the retrieval is approximate. The error in this approximation may lead to one of two
situations – a false drop occurs when some relevant document is not retrieved;
and a false positive occurs when some irrelevant document is retrieved. Thus,
for information-retrieval queries that mandate no loss of relevant information,
it is acceptable to have false positives, but not false drops.
22.17 Suppose you want to find documents that contain at least k of a given set of n
keywords. Suppose also you have a keyword index that gives you a (sorted) list
of identifiers of documents that contain a specified keyword. Give an efficient
algorithm to find the desired set of documents.
Answer: Let S be a set of n keywords. An algorithm to find all documents that
contain at least k of these keywords is given below :
This algorithm calculates a reference count for each document identifier. A
reference count of i for a document identifier d means that at least i of the keywords in S occur in the document identified by d. The algorithm maintains a
list of records, each having two fields – a document identifier, and the refer-
Total
relv.
0.0004
0.0029
0.0013
0.0029
0.0026
0.0054
0.0002
0.0015
0.0041
Exercises
239
ence count for this identifier. This list is maintained sorted on the document
identifier field.
initialize the list L to the empty list;
for (each keyword c in S) do
begin
D := the list of documents identifiers corresponding to c;
for (each document identifier d in D) do
if (a record R with document identifier as d is on list L) then
R.ref erence count := R.ref erence count + 1;
else begin
make a new record R;
R.document id := d;
R.ref erence count := 1;
add R to L;
end;
end;
for (each record R in L) do
if (R.ref erence count >= k) then
output R;
Note that execution of the second for statement causes the list D to “merge”
with the list L. Since the lists L and D are sorted, the time taken for this merge
is proportional to the sum of the lengths of the two lists. Thus the algorithm
runs in time (at most) proportional to n times the sum total of the number of
document identifiers corresponding to each keyword in S.
C H A P T E R
2 3
Advanced Data Types and
New Applications
This chapter covers advanced data types and new applications, including temporal
datababases, spatial and geographic databases, multimedia databases, and mobility
and personal databases. In particular, the data types mentioned above have grown in
importance in recent years, and commercial database systems are increasingly providing support for such data types through extensions to the database system variously called cartridges or extenders.
This chapter is suited as a means to lay the groundwork for an advanced course.
Some of the material, such as temporal and spatial data types, may be suitable for
self-study in a first course.
Changes from 3rd edition:
This material was part of Chapter 21 in the previous edition, but that chapter has
been split into two chapters, Chapters 22 and 23, in this edition.
Coverage of R-trees has been extended, with an informal description of insertion
and deletion algorithms. Coverage of mobile data communication has been updated.
Exercises
23.1 What are the two types of time, and how are they different? Why does it make
sense to have both types of time associated with a tuple?
Answer: A temporal database models the changing states of some aspects
of the real world. The time intervals related to the data stored in a temporal
database may be of two types - valid time and transaction time. The valid time
for a fact is the set of intervals during which the fact is true in the real world.
The transaction time for a data object is the set of time intervals during which
this object is part of the physical database. Only the transaction time is system
dependent and is generated by the database system.
Suppose we consider our sample bank database to be bitemporal. Only the
concept of valid time allows the system to answer queries such as - “What was
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Smith’s balance two days ago?”. On the other hand, queries such as - “What
did we record as Smith’s balance two days ago?” can be answered based on
the transaction time. The difference between the two times is important. For
example, suppose, three days ago the teller made a mistake in entering Smith’s
balance and corrected the error only yesterday. This error means that there is a
difference between the results of the two queries (if both of them are executed
today).
23.2 Will functional dependencies be preserved if a relation is converted to a temporal relation by adding a time attribute? How is the problem handled in a
temporal database?
Answer: Functional dependencies may be violated when a relation is augmented to include a time attribute. For example, suppose we add a time attribute to the relation account in our sample bank database. The dependency
account-number→balance may be violated since a customer’s balance would
keep changing with time.
To remedy this problem temporal database systems have a slightly different notion of functional dependency, called temporal functional dependency. For
τ
example, the temporal functional dependency account-number→balance over
Account-schema means that for each instance account of Account-schema, all snapshots of account satisfy the functional dependency account-number→balance; i.e
at any time instance, each account will have a unique bank balance corresponding to it.
23.3 Suppose you have a relation containing the x, y coordinates and names of
restaurants. Suppose also that the only queries that will be asked are of the
following form: The query specifies a point, and asks if there is a restaurant exactly at that point. Which type of index would be preferable, R-tree or B-tree?
Why?
Answer: The given query is not a range query, since it requires only searching
for a point. This query can be efficiently answered by a B-tree index on the pair
of attributes (x, y).
23.4 Consider two-dimensional vector data where the data items do not overlap.
Is it possible to convert such vector data to raster data? If so, what are the
drawbacks of storing raster data obtained by such conversion, instead of the
original vector data?
Answer: To convert non-overlapping vector data to raster data, we set the
values for exactly those pixels that lie on any one of the data items (regions);
the other pixels have a default value.
The disadvantages to this approach are: loss of precision in location information (since raster data loses resolution), a much higher storage requirement,
and loss of abstract information (like the shape of a region).
23.5 Suppose you have a spatial database that supports region queries (with circular regions) but not nearest-neighbor queries. Describe an algorithm to find the
nearest neighbor by making use of multiple region queries.
Exercises
243
Answer: Suppose that we want to search for the nearest neighbor of a point P
in a database of points in the plane. The idea is to issue multiple region queries
centered at P . Each region query covers a larger area of points than the previous query. The procedure stops when the result of a region query is non-empty.
The distance from P to each point within this region is calculated and the set
of points at the smallest distance is reported.
23.6 Suppose you want to store line segments in an R-tree. If a line segment is not
parallel to the axes, the bounding box for it can be large, containing a large
empty area.
• Describe the effect on performance of having large bounding boxes on
queries that ask for line segments intersecting a given region.
• Briefly describe a technique to improve performance for such queries and
give an example of its benefit. Hint: you can divide segments into smaller
pieces.
Answer:
R
Figure 21.17 a) : Representation of a Segment by One Rectangle
R
Figure 21.17 b) : Splitting each Segment into Four Pieces
Large bounding boxes tend to overlap even where the region of overlap
does not contain any information. The Figure 21.17 a) shows a region R within
which we have to locate a segment. Note that even though none of the four
segments lies in R, due to the large bounding boxes, we have to check each
of the four bounding boxes to confirm this. A significant improvement is ob-
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served in the Figure 21.17 b), where each segment is split into multiple pieces,
each with its own bounding box. In the second case, the box R is not part of the
boxes indexed by the R-tree. In general, dividing a segment into smaller pieces
causes the bounding boxes to be smaller and less wasteful of area.
23.7 Give a recursive procedure to efficiently compute the spatial join of two relations with R-tree indices. (Hint: Use bounding boxes to check if leaf entries
under a pair of internal nodes may intersect.)
Answer: Following is a recursive procedure for computing spatial join of two
R-trees.
SpJoin(node n1 , node n2 )
begin
if(the bounding boxes of n1 and n2 do not intersect)
return;
if(both n1 and n2 are leaves)
output all pairs of entries (e1 , e2 ) such that
e1 ∈ n1 and e2 ∈ n2 , and e1 and e2 overlap;
if(n1 is not a leaf)
N S1 = set of children of n1 ;
else
N S1 = { n1 };
if(n1 is not a leaf)
N S1 = set of children of n1 ;
else
N S1 = { n1 };
for each ns1 in N S1 and ns2 in N S2 ;
SpJoin(ns1 , ns2 );
end
23.8 Study the support for spatial data offered by the database system that you use,
and implement the following:
a. A schema to represent the geographic location of restaurants along with
features such as the cuisine served at the restaurant and the level of expensiveness.
b. A query to find moderately priced restaurants that serve Indian food and
are within 5 miles of your house (assume any location for your house).
c. A query to find for each restaurant the distance from the nearest restaurant
serving the same cuisine and with the same level of expensiveness.
Answer: TO BE SOLVED
23.9 What problems can occur in a continuous-media system if data is delivered
either too slowly or too fast?
Exercises
245
Answer: Continuous media systems typically handle a large amount of data,
which have to be delivered at a steady rate. Suppose the system provides the
picture frames for a television set. The delivery rate of data from the system
should be matched with the frame display rate of the TV set. If the delivery
rate is too low, the display would periodically freeze or blank out, since there
will be no new data to be displayed for some time. On the other hand, if the
delivery rate is too high, the data buffer at the destination TV set will overflow
causing loss of data; the lost data will never get displayed.
23.10 Describe how the ideas behind the RAID organization (Section 11.3) can be used
in a broadcast-data environment, where there may occasionally be noise that
prevents reception of part of the data being transmitted.
Answer: The concepts of RAID can be used to improve reliability of the broadcast of data over wireless systems. Each block of data that is to be broadcast
is split into units of equal size. A checksum value is calculated for each unit
and appended to the unit. Now, parity data for these units is calculated. A
checksum for the parity data is appended to it to form a parity unit. Both the
data units and the parity unit are then broadcast one after the other as a single
transmission.
On reception of the broadcast, the receiver uses the checksums to verify
whether each unit is received without error. If one unit is found to be in error, it can be reconstructed from the other units.
The size of a unit must be chosen carefully. Small units not only require
more checksums to be computed, but the chance that a burst of noise corrupts
more than one unit is also higher. The problem with using large units is that
the probability of noise affecting a unit increases; thus there is a tradeoff to be
made.
23.11 List three main features of mobile computing over wireless networks that are
distinct from traditional distributed systems.
Answer: Some of the main distinguishing features are as follows.
• In distributed systems, disconnection of a host from the network is considered to be a failure, whereas allowing such disconnection is a feature of
mobile systems.
• Distributed systems are usually centrally administered, whereas in mobile
computing, each personal computer that participates in the system is administered by the user (owner) of the machine and there is little central
administration, if any.
• In conventional distributed systems, each machine has a fixed location and
network address(es). This is not true for mobile computers, and in fact, is
antithetical to the very purpose of mobile computing.
• Queries made on a mobile computing system may involve the location and
velocity of a host computer.
• Each computer in a distributed system is allowed to be arbitrarily large
and may consume a lot of (almost) uninterrupted electrical power. Mobile
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systems typically have small computers that run on low wattage, shortlived batteries.
23.12 List three factors that need to be considered in query optimization for mobile
computing that are not considered in traditional query optimizers.
Answer: The most important factor influencing the cost of query processing in
traditional database systems is that of disk I/O. However, in mobile computing, minimizing the amount of energy required to execute a query is an important task of a query optimizer. To reduce the consumption of energy (battery
power), the query optimizer on a mobile computer must minimize the size and
number of queries to be transmitted to remote computers as well as the time
for which the disk is spinning.
In traditional database systems, the cost model typically does not include
connection time and the amount of data transferred. However, mobile computer users are usually charged according to these parameters. Thus, these parameters should also be minimized by a mobile computer’s query optimizer.
23.13 Define a model of repeatedly broadcast data in which the broadcast medium is
modeled as a virtual disk. Describe how access time and data-transfer rate for
this virtual disk differ from the corresponding values for a typical hard disk.
Answer: We can distinguish two models of broadcast data. In the case of a pure
broadcast medium, where the receiver cannot communicate with the broadcaster, the broadcaster transmits data with periodic cycles of retransmission of
the entire data, so that new receivers can catch up with all the broadcast information. Thus, the data is broadcast in a continuous cycle. This period of the
cycle can be considered akin to the worst case rotational latency in a disk drive.
There is no concept of seek time here. The value for the cycle latency depends
on the application, but is likely to be at least of the order of seconds, which is
much higher than the latency in a disk drive.
In an alternative model, the receiver can send requests back to the broadcaster. In this model, we can also add an equivalent of disk access latency, between the receiver sending a request, and the broadcaster receiving the request
and responding to it. The latency is a function of the volume of requests and
the bandwidth of the broadcast medium. Further, queries may get satisfied
without even sending a request, since the broadcaster happened to send the
data either in a cycle or based on some other receivers request. Regardless, latency is likely to be at least of the order of seconds, again much higher than the
corresponding values for a hard disk.
A typical hard disk can transfer data at the rate of 1 to 5 megabytes per
second. In contrast, the bandwidth of a broadcast channel is typically only a
few kilobytes per second. Total latency is likely to be of the order of seconds to
hundreds or even thousands of seconds, compared to a few milliseconds for a
hard disk.
23.14 Consider a database of documents in which all documents are kept in a central
database. Copies of some documents are kept on mobile computers. Suppose
that mobile computer A updates a copy of document 1 while it is disconnected,
Exercises
247
and, at the same time, mobile computer B updates a copy of document 2 while
it is disconnected. Show how the version-vector scheme can ensure proper updating of the central database and mobile computers when a mobile computer
reconnects.
Answer: Let C be the computer onto which the central database is loaded.
Each mobile computer (host) i stores, with its copy of each document d, a
version-vector – that is a set of version numbers Vd,i,j , with one entry for each
other host j that stores a copy of the document d, which it could possibly update.
Host A updates document 1 while it is disconnected from C. Thus, according to the version vector scheme, the version number V1,A,A is incremented by
one.
Now, suppose host A re-connects to C. This pair exchanges version-vectors
and finds that the version number V1,A,A is greater than V1,C,A by 1, (assuming
that the copy of document 1 stored host A was updated most recently only by
host A). Following the version-vector scheme, the version of document 1 at C
is updated and the change is reflected by an increment in the version number
V1,C,A . Note that these are the only changes made by either host.
Similarly, when host B connects to host C, they exchange version-vectors,
and host B finds that V1,B,A is one less than V1,C,A . Thus, the version number
V1,B,A is incremented by one, and the copy of document 1 at host B is updated.
Thus, we see that the version-vector scheme ensures proper updating of the
central database for the case just considered. This argument can be very easily
generalized for the case where multiple off-line updates are made to copies of
document 1 at host A as well as host B and host C. The argument for off-line
updates to document 2 is similar.
23.15 Give an example to show that the version-vector scheme does not ensure serializability. (Hint: Use the example from Exercise 23.14, with the assumption
that documents 1 and 2 are available on both mobile computers A and B, and
take into account the possibility that a document may be read without being
updated.)
Answer: Consider the example given in the previous exercise. Suppose that
both host A and host B are not connected to each other. Further, assume that
identical copies of document 1 and document 2 are stored at host A and host
B.
Let {X = 5} be the initial contents of document 1, and {X = 10} be the
initial contents of document 2. Without loss of generality, let us assume that all
version-vectors are initially zero.
Suppose host A updates the number its copy of document 1 with that in its
copy of document 2. Thus, the contents of both the documents (at host A) are
now {X = 10}. The version number V1,A,A is incremented to 1.
While host B is disconnected from host A, it updates the number in its copy
of document 2 with that in its copy of document 1. Thus, the contents of both
the documents (at host B) are now {X = 5}. The version number V2,B,B is
incremented to 1.
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Later, when host A and host B connect, they exchange version-vectors. The
version-vector scheme updates the copy of document 1 at host B to {X = 10},
and the copy of document 2 at host A to {X = 5}. Thus, both copies of each
document are identical, viz. document 1 contains {X = 10} and document 2
contains {X = 5}.
However, note that a serial schedule for the two updates (one at host A and
another at host B) would result in both documents having the same contents.
Hence this example shows that the version-vector scheme does not ensure serializability.
C H A P T E R
2 4
Advanced Transaction Processing
In this chapter, we go beyond the basic transaction processing schemes discussed previously, and cover more advanced transaction-processing concepts, including transaction-processing monitors, workflow systems, main-memory databases, real-time
transaction systems, and handling of long-duration transactions by means of nested
transactions, multi-level transactions and weak degrees of consistency. We end the
chapter by covering weak degrees of consistency used to handle multidatabase systems.
This chapter is suited to an advanced course. The sections on TP monitors and
workflows may also be covered in an introductory course as independent-study material.
Changes from 3rd edition:
Coverage of remote backup systems has been moved from this chapter to the chapter
on recovery, while coverage of transaction processing in multidatabases has been
moved into this chapter from its earlier position in the distributed database chapter.
Exercises
24.1 Explain how a TP monitor manages memory and processor resources more effectively than a typical operating system.
Answer: In a typical OS, each client is represented by a process, which occupies a lot of memory. Also process multi-tasking over-head is high.
A TP monitor is more of a service provider, rather than an environment for
executing client processes. The client processes run at their own sites, and they
send requests to the TP monitor whenever they wish to avail of some service.
The message is routed to the right server by the TP monitor, and the results of
the service are sent back to the client.
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The advantage of this scheme is that the same server process can be serving several clients simultaneously, by using multithreading. This saves memory space, and reduces CPU overheads on preserving ACID properties and
on scheduling entire processes. Even without multi-threading, the TP monitor
can dynamically change the number of servers running, depending on whatever factors affect good performance. All this is not possible with a typical OS
setup.
24.2 Compare TP monitor features with those provided by Web servers supporting
servlets (such servers have been nicknamed TP-lite).
Answer: TO BE FILLED IN.
24.3 Consider the process of admitting new students at your university (or new
employees at your organization).
a. Give a high-level picture of the workflow starting from the student application procedure.
b. Indicate acceptable termination states, and which steps involve human intervention.
c. Indicate possible errors (including deadline expiry) and how they are dealt
with.
d. Study how much of the workflow has been automated at your university.
Answer: TO BE FILLED IN.
24.4 Like database systems, workflow systems also require concurrency and recovery management. List three reasons why we cannot simply apply a relational
database system using 2PL, physical undo logging, and 2PC.
Answer:
a. The tasks in a workflow have dependencies based on their status. For example the starting of a task may be conditional on the outcome (such as
commit or abort) of some other task. All the tasks cannot execute independently and concurrently, using 2PC just for atomic commit.
b. Once a task gets over, it will have to expose its updates, so that other tasks
running on the same processing entity don’t have to wait for long. 2PL is
too strict a form of concurrency control, and is not appropriate for workflows.
c. Workflows have their own consistency requirements, i.e. failure-atomicity.
An execution of a workflow must finish in an acceptable termination state.
Because of this, and because of early exposure of uncommitted updates,
the recovery procedure will be quite different. Some form of logical logging and compensation transactions will have to be used. Also to perform
forward recovery of a failed workflow, the recovery routines need to restore the state information of the scheduler and tasks, not just the updated
data items. Thus simple WAL cannot be used.
24.5 If the entire database fits in main memory, do we still need a database system
to manage the data? Explain your answer.
Exercises
251
Answer: Even if the entire database fits in main memory, a DBMS is needed
to perform tasks like concurrency control, recovery, logging etc, in order to
preserve ACID properties of transactions.
24.6 Consider a main-memory database system recovering from a system crash.
Explain the relative merits of
• Loading the entire database back into main memory before resuming transaction processing
• Loading data as it is requested by transactions
Answer:
• Loading the entire database into memory in advance can provide transactions which need high-speed or realtime data access the guarantee that
once they start they will not have to wait for disk accesses to fetch data.
However no transaction can run till the entire database is loaded.
• The advantage in loading on demand is that transaction processing can
start rightaway; however transactions may see long and unpredictable delays in disk access until the entire database is loaded into memory.
24.7 In the group-commit technique, how many transactions should be part of a
group? Explain your answer.
Answer: As log-records are written to stable storage in multiples of a block, we
should group transaction commits in such a way that the last block containing
log-records for the current group is almost full.
24.8 Is a high-performance transaction system necessarily a real-time system? Why
or why not?
Answer: A high-performance system is not necessarily a real-time system.
In a high performance system, the main aim is to execute each transaction as
quickly as possible, by having more resources and better utilization. Thus average speed and response time are the main things to be optimized. In a real-time
system, speed is not the central issue. Here each transaction has a deadline, and
taking care that it finishes within the deadline or takes as little extra time as
possible, is the critical issue.
24.9 In a database system using write-ahead logging, what is the worst-case number of disk accesses required to read a data item? Explain why this presents a
problem to designers of real-time database systems.
Answer: In the worst case, a read can cause a buffer page to be written to disk
(preceded by the corresponding log records), followed by the reading from
disk of the page containing the data to be accessed. This takes two or more
disk accesses, and the time taken is several orders of magnitude more than the
main-memory reference required in the best case. Hence transaction executiontime variance is very high and can be estimated only poorly. It is therefore
difficult to plan schedules which need to finish within a deadline.
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24.10 Explain why it may be impractical to require serializability for long-duration
transactions.
Answer: In the presence of long-duration transactions, trying to ensure serializability has several drawbacks:a. With a waiting scheme for concurrency control, long-duration transactions
will force long waiting times. This means that response time will be high,
concurrency will be low, so throughput will suffer. The probability of deadlocks is also increased.
b. With a time-stamp based scheme, a lot of work done by a long-running
transaction will be wasted if it has to abort.
c. Long duration transactions are usually interactive in nature, and it is very
difficult to enforce serializability with interactiveness.
Thus the serializability requirement is impractical. Some other notion of database
consistency has to be used in order to support long duration transactions.
24.11 Consider a multithreaded process that delivers messages from a durable queue
of persistent messages. Different threads may run concurrently, attempting to
deliver different messages. In case of a delivery failure, the message must be
restored in the queue. Model the actions that each thread carries out as a multilevel transaction, so that locks on the queue need not be held till a message is
delivered.
Answer: Each thread can be modeled as a transaction T which takes a message from the queue and delivers it. We can write transaction T as a multilevel
transaction with subtransactions T1 and T2 . Subtransaction T1 removes a message from the queue and subtransaction T2 delivers it. Each subtransaction releases locks once it completes, allowing other transactions to access the queue.
If transaction T2 fails to deliver the message, transaction T1 will be undone
by invoking a compensating transaction which will restore the message to the
queue.
24.12 Discuss the modifications that need to be made in each of the recovery schemes
covered in Chapter 17 if we allow nested transactions. Also, explain any differences that result if we allow multilevel transactions.
Answer:
• The advanced recovery algorithm of Section 17.9 :The redo pass, which repeats history, is the same as before. We discuss
below how the undo pass is handled.
Recovery with nested transactions:
Each subtransaction needs to have a unique TID, because a failed
subtransaction might have to be independently rolled back and restarted.
If a subtransaction fails, the recovery actions depend on whether the
unfinished upper-level transaction should be aborted or continued. If it
should be aborted, all finished and unfinished subtransactions are undone by a backward scan of the log (this is possible because the locks
on the modified data items are not released as soon as a subtransaction finishes). If the nested transaction is going to be continued, just
Exercises
253
the failed transaction is undone, and then the upper-level transaction
continues.
In the case of a system failure, depending on the application, the entire nested-transaction may need to be aborted, or, (for e.g., in the case
of long duration transactions) incomplete subtransactions aborted, and
the nested transaction resumed. If the nested-transaction must be aborted,
the rollback can be done in the usual manner by the recovery algorithm, during the undo pass. If the nested-transaction must be restarted,
any incomplete subtransactions that need to be rolled back can be rolled
back as above. To restart the nested-transaction, state information about
the transaction, such as locks held and execution state, must have been
noted on the log, and must restored during recovery. Mini-batch transactions (discussed in Section 21.2.7) are an example of nested transactions that must be restarted.
Recovery with multi-level transactions:
In addition to what is done in the previous case, we have to handle
the problems caused by exposure of updates performed by committed
subtransactions of incomplete upper-level transactions. A committed
subtransaction may have released locks that it held, so the compensating transaction has to reacquire the locks. This is straightforward in
the case of transaction failure, but is more complicated in the case of
system failure.
The problem is, a lower level subtransaction a of a higher level transaction A may have released locks, which have to be reacquired to compensate A during recovery. Unfortunately, there may be some other
lower level subtransaction b of a higher level transaction B that started
and acquired the locks released by a, before the end of A. Thus undo
records for b may precede the operation commit record for A. But if b
had not finished at the time of the system failure, it must first be rolled
back and its locks released, to allow the compensating transaction of A
to reacquire the locks.
This complicates the undo pass; it can no longer be done in one
backward scan of the log. Multilevel recovery is described in detail in
David Lomet, “MLR: A Recovery Method for Multi-Level Systems”,
ACM SIGMOD Conf. on the Management of Data 1992, San Diego.
• Recovery in a shadow paging scheme :In a shadow paging based scheme, the implementation will become
very complicated if the subtransactions are to be executed concurrently. If
they are to execute serially, the current page table is copied to the shadow
page table at the end of every subtransaction. The general idea of recovery
then is alike to the logging based scheme, except that undoing and redoing
become much easier, as in Section 17.5.
24.13 What is the purpose of compensating transactions? Present two examples of
their use.
Answer: A compensating transaction is used to perform a semantic undo of
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changes made previously by committed transactions. For example, a person
might deposit a check in their savings account. Then the database would be
updated to reflect the new balance. Since it takes a few days for the check to
clear, it might be discovered later that the check bounced, in which case a compensating transaction would be run to subtract the amount of the bounced
check from the depositor’s account. Another example of when a compensating transaction would be used is in a grading program. If a student’s grade on
an assignment is to be changed after it is recorded, a compensating program
(usually an option of the grading program itself) is run to change the grade
and redo averages, etc.
24.14 Consider a multidatabase system in which it is guaranteed that at most one
global transaction is active at any time, and every local site ensures local serializability.
a. Suggest ways in which the multidatabase system can ensure that there is
at most one active global transaction at any time.
b. Show by example that it is possible for a nonserializable global schedule
to result despite the assumptions.
Answer:
a. We can have a special data item at some site on which a lock will have
to be obtained before starting a global transaction. The lock should be released after the transaction completes. This ensures the single active global
transaction requirement. To reduce dependency on that particular site being up, we can generalize the solution by having an election scheme to
choose one of the currently up sites to be the co-ordinator, and requiring
that the lock be requested on the data item which resides on the currently
elected co-ordinator.
b. The following schedule involves two sites and four transactions. T1 and T2
are local transactions, running at site 1 and site 2 respectively. TG1 and TG2
are global transactions running at both sites. X1 , Y1 are data items at site 1,
and X2 , Y2 are at site 2.
T1
write(Y1 )
T2
TG1
TG2
read(Y1 )
write(X2 )
read(X2 )
write(Y2 )
read(Y2 )
write(X1 )
read(X1 )
In this schedule, TG2 starts only after TG1 finishes. Within each site, there
is local serializability. In site 1, TG2 → T1 → TG1 is a serializability order.
Exercises
255
In site 2, TG1 → T2 → TG2 is a serializability order. Yet the global schedule
schedule is non-serializable.
24.15 Consider a multidatabase system in which every local site ensures local serializability, and all global transactions are read only.
a. Show by example that nonserializable executions may result in such a system.
b. Show how you could use a ticket scheme to ensure global serializability.
Answer:
a. The same system as in the answer to Exercise 24.14 is assumed, except
that now both the global transactions are read-only. Consider the schedule
given below.
T1
T2
TG1
TG2
read(X1 )
write(X1 )
read(X1 )
read(X2 )
write(X2 )
read(X2 )
Though there is local serializability in both sites, the global schedule is
not serializable.
b. Since local serializability is guaranteed, any cycle in the system wide precedence graph must involve at least two different sites, and two different
global transactions. The ticket scheme ensures that whenever two global
transactions access data at a site, they conflict on a data item (the ticket)
at that site. The global transaction manager controls ticket access in such
a manner that the global transactions execute with the same serializability
order in all the sites. Thus the chance of their participating in a cycle in the
system wide precedence graph is eliminated.
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