Relational Algebra

Relational Algebra

• Set operations: Union, intersection, difference, Cartesian product

• Relational operations: Selection, projection, join, division

Union

• Set1={A, B, C}

• Set2={C, D, E}

• Union: Members in Set 1 or in Set 2– Set1 U Set 2 = {A, B, C, D, E}

• Or

Intersect

• Members in Set 1 and in Set 2– Set1 ∩ Set2={C}

• And

Difference

• Set1 – Set2: Members in Set1 but not in set2 = {A,B}

• Set2 – Set1:Members in Set2 but not in set1 = {D, E}

• Set1-Set2 ≠ Set2 – Set1

Union Compatibility

• Two relations that have the same number of attributes and same type of attributes.

• Union, Intersect and difference operators require the two relations to be union compatible.

• File 1: – SID – 9 characters– Sname – 25 characters

• File 2:– SSN – 9 characters– Ename – 25 characters

• File 3:– Ename – 25 characters– EID – 9 characters

Use Union and Difference to Simulate Intersect

• Set1 ∩ Set2 = Set1 – (Set1 – Set2)

Venn DiagramSet 1: Major = ‘Business’

Set 2: Sex = ‘F’

Set 3: GPA > 3.0

Files as Sets

• Business students’ file: BusSt• Science student’s file: SciSt

– BusSt U SciSt:– BusSt ∩ SciSt– BusSt – SciSt

• Spring 04 Student file: S04St• Fall 04 Student file: F04St

– S04St – F04St– F04St – S04St

Product

• Set1 = {a, b, c}

• Set2 = {X, Y, Z}

• Set1 X Set2 = {aX, aY aZ, bX, bY, bZ, cX, cY, cZ}

• Faculty File: • FID Fname• F1 Chao• F2 Smith

• Student File:• SID Sname FID• S1 Peter F1• S2 Paul F2• S3 Smith F1

• Faculty X Student:

Selection

• Selection operation works on a single relation and defines a relation that contains records that satisfy the criteria.

– σ criteria ( Relation)

– σ Major = ‘Bus’ AND GPA > 3.0 (Student)

Projection

• Projection operation works on a single relation and defines a vertical subset of the relation, extracting the values of specified attributes and eliminating duplicates.

• π a1, a2, … (Relation)

• π sid, sname (Student)

• Student file: • SID, Sname Sex Major• S1 Peter M Bus• S2 Paul M Art• S3 Mary F Bus• S4 Nancy F Sci• S5 Peter M Art

• π sid, sname (Student)• π sname, sex (Student)

• π sname, sex (σ Major = ‘Bus’ (Student))

• σ Major = ‘Bus’ (π sname, sex (Student))

Duplications due to Projection• WorkLog file:

• EID PjID Hours• E1 P2 5• E1 P1 4• E2 P2 6• E2 P1 8• E3 P1 4

• π eid (WorkLog)• Relation contrains: no duplication• Eliminating duplicates may cause problems:

– π Hours (σ PjID = ‘P1 (WorkLog))• In practice, users determine whether to eliminate

duplicates:– SELECT DISTINCT EID FROM WorkLog;– SELECT HOURS FROM WorkLog WHERE PjID = ‘P1’;

Natural Join

• The two relations must have common attributes.

• Combines two relations to form a new relation where records of the two relations are combined if the common attributes have the same value. One occurrence of each common attribute is eliminated.

Faculty File: FID FnameF1 ChaoF2 Smith

Student File:SID Sname FIDS1 Peter F1S2 Paul F2S3 Smith F1

Faculty Join Student =

π All except the duplicated attributes (σ Faculty.FID = Student.FID (Faculty X Student))

Note: Use RelationName.FieldName to make a field name unique.

Examples

• University database:– Student: SID, Sname, Sex, Major, GPA, FID– Account: SID, Balance– Faculty: FID, Fname– Course: CID, Cname, Credits– StudentCourse: SID, CID