Relational Algebra

A presentation for CS 457By Dawn Haddan

Overview

What is relational algebra?– A collection of operations to:

• Manipulate relations (tables)• Specify Queries

Application to Databases– Used to perform many common requests in

the relational database model

Definitions

Relational Data Model– Represents the database as a collection of relations

Relation– For our purposes, a table of values containing rows, where each

row is a collection of related values. Tuple

– A row in a table Attribute

– A column header in a table Domain

– A set of values each attribute can take on

Relational Algebra Operations

Basic operations– SELECT– PROJECT

Set Theoretic Operations– UNION– INTERSECTION– CARTESIAN PRODUCT

Database-Specific Operation– JOIN

Basic Operations

SELECT– Selects a subset of tuples (rows) from a

relation (table) based upon a boolean selection condition

PROJECT– Selects only attributes (columns) of interest

from a table

Select General form:

– σ<SELECTION CONDITION>(R)• With…..

– σ as the symbol denoting a selection operation

– SELECTION CONDITION equating to a boolean value

– R representing a relational algebra expression that results in a relation, most frequently the name of a relation (table)

Select Example Given the relation (table) named STUDENT:

The SELECT operation σAGE>19(STUDENT) would return the new relation:

Name Sex Age Year

Alice F 25 SOPH

Jacob M 19 FROSH

Emily F 20 JUNIOR

Name Sex Age Year

Alice F 25 SOPH

Emily F 20 JUNIOR

Project General form:

– π<ATTRIBUTE LIST>(R)• With…..

– π as the symbol denoting a PROJECT operation

– ATTRIBUTE LIST as a list of attributes (columns) from the relation R

– R representing a relational algebra expression that results in a relation, most frequently the name of a relation (table)

– Result• A relation containing only the attributes specified in the

order specified• At most the number of tuples (rows) in the original

relation– duplicate tuples would constitute an invalid relation

Project Example Given the relation (table) named STUDENT:

The PROJECT operation πYEAR,SEX(STUDENT) would return the new relation:

Where the duplicate tuple has been removed and the attributes appear in the order specified in the attribute list

Name Sex Age Year

Alice F 25 SOPH

Jacob M 19 FROSH

Emily F 20 SOPH

Year Sex

SOPH F

FROSH M

Set Theoretic Operations Both UNION and INTERSECTION …

– Are binary operations– Return a single relation– Must be union compatible

• The two relations must have the same tuple types

UNION– Produces a relation composed of all the tuples

(rows) in either of the original relations INTERSECTION

– Produces a relation composed of all the tuples (rows) that exist in both of the original relations

Set Theoretic Operations

CARTESIAN PRODUCT– Binary operation– Relations not necessarily union compatible– Combines tuples (rows) from two relations, say R

and S– Result is a new relation whose attributes are the

attributes from R and the attributes from S– Result contains the combined tuples from R and

S. For instance, if R has 6 tuples, and S has 5 tuples, the result will contain 30 tuples.

Sequences of Operations

Allows application of several operations

Produces a single relational algebra expression

Sequence of Operations Example Given the relation (table) named STUDENT:

The operation πNAME,AGE,SEXσAGE>21 OR SEX=‘M’(STUDENT) would return the new relation:

Where the OR implies a UNION operation

NAME SEX AGE YEAR

Alice F 25 SOPH

Jacob M 19 FROSH

Emily F 20 JUNIOR

Name Age Sex

Alice 25 F

Jacob 19 M

Join

Simply a CARTESIAN PRODUCT of two relations (tables) followed by a SELECT

Combines tuples based upon the comparison of one or more attributes

Allows us to process relationships between relations

Join

General form:

– R |><|<JOIN CONDITION>S

– Where…• R and S are relations• |><| symbolizes the JOIN operation• JOIN CONDITION is specified on attributes of both R

and S and evaluated for each combination of tuples Result

– A new relation • Set of attributes is the union of all the attributes for R and S

• Contains combinations of tuples that satisfy the join condition

Join Example (Slide 1) Given the relation (table) named STUDENT:

And the relation (table) named ADVISOR:

And the JOIN operation… πSNAME,ANAME,PHONE(STUDENT|><|

AID=IDADVISOR)

ID SNAME AID

123 Tom 333

456 Bobo 444

789 Phil 333

ID ANAME PHONE DEPT

333 Joe 777-9987 CS

444 John 888-9876 CE

555 Jim 567-9876 ME

Join Example (Slide 2) Returns the following relation:

SNAME ANAME PHONE

Tom Joe 777-9987

Bobo John 888-9876

Phil Joe 777-9987

SQL equivalent statements

σAGE>19(STUDENT)– SELECT * FROM STUDENT WHERE AGE>19;

πYEAR,SEX(STUDENT)– SELECT YEAR,SEX FROM STUDENT;

πNAME,AGE,SEXσAGE>21 OR SEX=‘M’(STUDENT)– SELECT NAME,AGE,SEX FROM STUDENT WHERE AGE>21 or

SEX=‘M’; πSNAME,ANAME,PHONE(STUDENT|><|AID=IDADVISOR)

– SELECT SNAME,ANAME,PHONE FROM STUDENT INNER JOIN ADVISOR ON ID=AID;

--- OR ---

– SELECT SNAME,ANAME,PHONE FROM STUDENT,ADVISOR WHERE ID=AID;

Conclusions

Questions?

www.cs.unr.edu/~haddan

Ted Codd, founder of relational algebra