CS634 Information Systems Dr Deepak B Phatak Subrao Nilekani Chair Professor Kanwal Rekhi Building, Department of CSE IIT Bombay Session 3, Relational

CS634 Information Systems

Dr Deepak B PhatakSubrao Nilekani Chair Professor

Kanwal Rekhi Building, Department of CSEIIT Bombay

Session 3, Relational Model

CS634-Session 3 Relational ModelDr. Deepak B Phatak 2

IIT BOMBAY

Session overview

• Review of earlier sessions• Introduction to relational model• Group projects


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sroll

Entity model

Student

snameshostel

sroomscpi

scourses

shobbies


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Table representation

sroll sname shostel

78011012 Ajay Shah 02

73815034 Nandan Nilekani 08

… … …


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ccode

Course entity

Course

cname

cstudents

cfaculty

ccredits


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TABLE REPRESENTATION

ccode cname ccredit

CS634 Modern Info Systems 06CS101 Computer Programming 08

…

……


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Student and course association

Student Set Course Set

980140129801401599057943990579619910149199112345

CS634

CS101

ME203

EE102


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Relationship set

Student

Registers For

Course

sroll

ccode


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Relationship set attribute(s)

Student

Registers For

Course

sroll

ccode

Grade


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Introduction to relational model

• Developed by professor Codd• Part of system-R work at IBM - 1972

• Mathematical foundation for database modeling

• Relational algebra and calculus• Structured Query Language (SQL)

• Structured English-like … (SEQUEL)


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Relational model

• A relation is a set of n-tuples• Rows in a table

• Each relation has a schema• List of attributes• Similar to column headers in a table


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Sample relation schema

• Student = (sroll, sname, sh, sr, scpi)• Course = (ccode, cname, ccredit)• Reg = (sroll, ccode, grade)


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Student relation

Student Set Course Set

98014012 …98014015 …99057943 …99057961 …99101491 …99112345 …

Number of elements = no. of students

- Each element is a 5-tuple


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Student relation as a Table

sroll sname sh

78011012 Ajay Shah 02

73815034 Nandan Nilekani 08

… … …


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Relational algebra

• A relation is an element• Operators are defined over relation(s) • A relational operation results in a new

relation having• Different set of rows• Different schema (may be)• Or both


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Keys

• Super key: A set of attributes that uniquely characterizes a specific n-tuple

• Candidate key: minimal super key• Primary key: chosen candidate key


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Examples of keys

Student (sroll, sname, sh, sr, scpi)• Superkeys: (unique entity identifier)

Sroll; Sroll + sname;Sh + sr; Sroll + sh + sr; …

• Candidate keys are reduced minimal superkeys

Sroll; sh + sr (single occupancy assumption)

• Primary key: sroll (practical choice)


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Sample relation

sroll sname sh

06011012 Vijay Ambre 02

sr scpi

218 8.49

06D15034 Parag Samarth

08 7.94218

06012015 Arul Menezes 03 146 9.25

06012018 Ajay Shah 03 151 8.38

06012014 Rajan Tambe 08 317 6.85


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Sample relation

sroll sname sh


sr

01D15034 Shaukat Ali 08

scpi

218 8.497.94218

98012015 Arul Menezes 03 146 9.2598012018 Ajay Shah 03 151 8.3898012014 Rajan Tambe 08 317 7.2598012019 Sanjay Mistry 07 169 6.85


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Sample relation

sroll sname sh


sr


scpi

218 8.497.94218

98012015 Arul Menezes 03 146 9.2598012018 Ajay Shah 03 151 8.3898012014 Rajan Tambe 08 317 7.2598012019 Sanjay Mistry 07 169 6.85


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Relations

• If any value in a table (or a file) changes (add, delete, update), such a change can be made in the same table or file

• However, a relational operation results in a new relation

• Relational algebra operations are used to extract meaningful information from one or more relations

• Can be directly mapped into SQL


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Relational algebra operators

• Selection• Get rows from a relation

• Projection• Get columns from a relation

• Cross product• Combine rows from multiple relations

• Join• Get meaningful information from the

cross product


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Selection

• Extracts n-tuples from a relation R, based on a predicate (condition) P

• R1 = p (R)

• R1: has the same schema as that of R• P: valid condition on R


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Selection

R1 = scpi > 9 AND sh = 3 (student)

The resulting relation will have one row [98012015 arul menezes 03 146 9.25]

SQL query for this relational operation can be written as

Select * From student Where scpi > 9 and sh = 3; ‘*’ means select ALL attributes of the schema


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Projection

• Projects only specified attributes• Given as a list

• R1 = list (R)

• R1 has a new schema• Cardinality (no of rows) ?


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Projection

R1 = cname, ccredit (course)

SQL query can be written as

Select cname, ccreditfrom Course;

cname ccreditInformation Systems 6Data Mining 6Professional Ethics in IT 3


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Projection- another example

R1 = sh (student)

SQL query: Select sh From student;

How many elements would R1 have?


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Projection example

sroll sname sh


sr


scpi

218 8.497.94218

98012015 Arul menezes 03 146 9.2598012018 Ajay Shah 03 151 8.3898012014 Rajan Tambe 08 317 6.85


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SQL implementation of projection

Select distinct sh From student;Result: Sh 2 8 3


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Expressions

Sname ( scpi >9 & sh = 8 (student))

Select sname From student Where scpi > 9 And sh = 8;


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CROSS PRODUCT

• Operates on two relations• R = R1 x R2• Concatenates each tuple of R1 with

every tuple of R2• If there are M and N elements in the

two relations, the resultant relation has M x N elements

• Schema of R is concatenation of the two schemas of R1 and R2• R1.A1, R1.A2, … , R2.A1, …, etc..


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Example tables

sroll sname - -

89005012 Sunita Sarawagi - -

89007017 Kesav Nori - -

89004039 Muthukrishnan - -

- - - -

sroll ccode -

89005012 CS413 -

89005012 CS634 -

89007017 CS634 -

89007017 CS413 - 89004039 HS412 -

- - -

Student

Reg


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Cross product

sroll sname --- --- Reg.sroll ccode -

89005012 Sunita Sarawagi - - 89005012 CS413 -89005012 Sunita Sarawagi - - 89005012 CS634 -

89005012 Sunita Sarawagi - - 89007017 CS634 -


89005012 Sunita Sarawagi - - 89004039 HS412 -

89007017 Kesav Nori - - 89005012 CS413 -

89007017 Kesav Nori - - 89005012 CS634 -

89007017 Kesav Nori - - 89007017 CS634 -

Student X Reg(First 8 Rows)


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Cross product

sroll sname --- --- sroll ccode -

89005012 Sunita Sarawagi - - 89005012 CS413 -89005012 Sunita Sarawagi - - 89005012 CS634 -



89005012 Sunita Sarawagi - - 89004039 HS412 -

89007017 Kesav Nori - - 89005012 CS413 -

89007017 Kesav Nori - - 89005012 CS634 -

89007017 Kesav Nori - - 89007017 CS634 -

Student X Reg(First 8 Rows)


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Join

• Join is defined to get meaningful set of rows from a cross product

• R = ρ (R1 X R2)

• Selection predicate provides for meaningful information extraction

• Two categories of join• Natural join• Theta join


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Natural join

• Ensures equality of values of all common attributes

• Result schema is union of two schemas

• R = r1 |x| r2

R = student |X| reg

R = student.Sroll =reg.Sroll (student X reg)


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sroll sname --- --- sroll ccode

89005012 Sunita Sarawagi - - 89005012 CS413 89005012 Sunita Sarawagi - - 89005012 CS634

89005012 Sunita Sarawagi - - 89007017 CS634

89005012 Sunita Sarawagi - - 89007017 CS413

89005012 Sunita Sarawagi - - 89004039 HS412

89007017 Kesav Nori - - 89005012 CS413

89007017 Kesav Nori - - 89005012 CS634

89007017 Kesav Nori - - 89007017 CS634

Cross product Student X Reg(First 8 Rows)


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SQL query for natural join

Select * from student natural join reg; Select * from student, reg Where student.Sroll = reg.Sroll;


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Natural join schema

sroll sname --- --- sroll ccode

89005012 Sunita Sarawagi - - 89005012 CS413 -89005012 Sunita Sarawagi - - 89005012 IT640 -

89007017 Kesav Nori - - 89007017 IT640 -

89007017 Kesav Nori - - 89007017 CS413 -

89004039 Muthukrishnan - - 89004039 HS412 -

Student |X| Reg


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Theta join

• R = R1 |x| R2

• Theta is any (meaningful) predicate• Usually has a “join” condition

• R = (R1 x R2)

• R = student |x| reg : student.sroll = reg.sroll and scpi > 9 and sh = 8


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SQL query for join

Select * from student, reg Where Student.Sroll = reg.Sroll and scpi > 9 and sh = 8;

Documents

CS634 Information Systems Dr Deepak B Phatak Subrao Nilekani Chair Professor Kanwal Rekhi Building, Department of CSE IIT Bombay Session 3, Relational