Chapter 3 Section 3.4
3
Relational Database Operators
(Relational Algebra)
Database Systems: Design, Implementation, and Management
7th Edition
Peter Rob & Carlos Coronel
What is Relational Algebra?
3
 Part of Relational DB Theory
 Operations that any RDBMS should provide for data
manipulation
 NOT directly included in products; capabilities generally
provided via QBE or SQL
What is included in RA?
3




Set Operations
Operations specific to RDBs
Recent Advanced Add-Ons
All RA operations work on one or more relations, and
produce a relation as a result
UNION
3
 Produces a resulting relation that contains a tuple for
every tuple in either or both of two input relations
(duplicates only occur once)
 The Relations being combined must be unioncompatible (type-compatible)
 e.g. CurrentEnrollments U HistoricalEnrollments;
MailListFromSierraClub U MailListFromAudabonSoc;
INTERSECTION
3
 Produces a resulting relation that contains a tuple for
every tuple in BOTH of two input relations
 The Relations being combined must be union-compatible
(type-compatible)
 MailListFromSierraClub INTERSECT
MailListFromNewBabyMag;
SET DIFFERENCE (MINUS)
3
 Produces a resulting relation that contains a tuple for
every tuple in FIRST of two input relations AND NOT IN
the second.
 The Relations being combined must be union-compatible
(type-compatible)
 MailListFromMarketingCompany - CurrentCustomerList;
CARTESIAN PRODUCT
(TIMES)
3
 Produces a resulting relation that contains all attributes in
either input relation and a tuple for every possible
combination of tuples in two input relations.
 The Relations being combined must be productcompatible
 BY ITSELF, not usually useful in the real world
Relational Database Operators
 PRODUCT produces a list of all possible
pairs of rows from two tables.
3
(old) Figure 2.8 PRODUCT
RESTRICT/SELECT
3
 Produces a resulting relation, containing only the tuples
that meet some condition (hence a “horizontal” subset of
the original relation)
 e.g. employees in department #4, students majoring in
CS, students with a GPA < 2.0
PROJECTion
3
 Produces a resulting relation, containing only the
attributes that are requested (hence a “vertical” subset of
the original relation)
 e.g. last name, first name and salary of employees; last
name, major, year of students; dept, class of sections
Relational Database Operators
3
 JOIN allows us to combine information from
two or more tables.
 JOIN is the real power behind the relational
database, allowing the use of independent
tables linked by common attributes.
JOINS
3
 Produces a resulting relation that contains all attributes
in either input relation and a tuple for “every possible
combination of tuples in two input relations that meet
some condition”.
Relational Database Operators
 Natural
3
JOIN links tables by selecting only
the rows with common values in their
common attribute(s). It is the result of a
three-stage process:

A PRODUCT of the tables is created. (Figure 3.12)

A SELECT is performed on the output of the first
step to yield only the rows for which the common
attribute values match. (Figure 3.13)

A PROJECT is performed to yield a single copy of
each attribute, thereby eliminating the duplicate
column. (Figure 3.14)
Natural Join, Step 1: PRODUCT
3
Natural Join, Step 2: SELECT
3
Natural Join, Step 3: PROJECT
3
Natural Join (continued)
 Final outcome yields table that
3

Does not include unmatched pairs

Provides only copies of matches
 If no match is made between the table rows,

the new table does not include the unmatched row
Relational Database Operators
3

EquiJOIN links tables based on an equality condition
that compares specified columns of each table. The
outcome of the EquiJOIN does not eliminate duplicate
columns and the condition or criteria to join the
tables must be explicitly defined.

Theta JOIN is an equiJOIN that compares specified
columns of each table using a comparison operator
other than the equality comparison operator.

In an Outer JOIN, the unmatched pairs would be
retained and the values for the unmatched other
tables would be left blank or null.
Outer Join
 Matched pairs are retained and any unmatched values in
other table are left null
 In outer join for tables CUSTOMER and AGENT, three
scenarios are possible:
3

Left outer join


Right outer join


Yields all rows in CUSTOMER table, including those that do not have a
matching value in the AGENT table
Yields all rows in AGENT table, including those that do not have
matching values in the CUSTOMER table
FULL OUTER JOIN - keeps all tuples in first or second relation
even if no matching tuples
Left Outer Join
3
Right Outer Join
3
DIVISION
3
 Useful for finding all X who are doing something with all
Y
 e.g. find all students who are taking all three of these
sections: 66416, 66417,66419
 book e.g. find all locations that are associated with both
codes A & B
Relational Database Operators
 DIVIDE typically involves the use of one single-column
table and one two-column table.
3
A Minimally Complete Set of RA Operations
3





RESTRICT,
PROJECT,
UNION,
SET DIFFERENCE,
CARTESIAN PRODUCT
 Others can be derived

R INTERSECT S is equivalent to (R U S) - ((R -S) U (S - R))
 Theta JOIN is equivalent to cartesian product followed by restrict
 NATURAL JOIN is equivalent to Cartesian product preceded by
rename and followed by project and restrict
Enhancements
3
 Aggregate Functions - SUM, AVERAGE, MAXIMUM,
MINIMUM
 Aggregates within Group
 e.g. GROUPING BY: Dept#; COUNT SSN, AVERAGE
SALARY (Employee) - for each department give the count
of # employees and the average salary
A Final Word
3
While RA is not seen commercially, it is a
foundation on what is available commercially. It is a
commonly understood basis for comparison and for
communication.
End Relational Algebra
3