Relational Query Operators (Algebra)

Relational Query Operators 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} Logical operator OR –Major = ‘CIS’ OR Major = ‘Acct’ –JobSkill = ‘Java’ OR JobSkill = ‘VB’

Intersect Members in Set 1 and in Set 2 –Set1 ∩ Set2={C} Logical operator AND –Major = ‘CIS’ AND GPA > 3.0 –JobSkill = ‘Java’ AND Experience > 5 –Note: Major = ‘CIS’ AND Major = ‘Acct’ is nonsense

Difference Set1={A, B, C} Set2={C, D, E} 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 Logical operator: NOT

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.

Union Compatibility Examples File 1: –SID – 9 characters –Sname – 25 characters File 2: –SSN – 9 characters –Ename – 25 characters File 3: –Ename – 25 characters –EID – 9 characters File 1 and file 2 are union compatible; file 1 and file 3 are not; file 2 and file 3 are not.

Use Union and Difference to Simulate Intersect Set1 ∩ Set2 = Set1 – (Set1 – Set2)

Venn Diagram Set 1: Young: Age<30 Set 2: Rich: Income>100,000’ Set 3: Smart: IQ > 150

Files as Sets Business students’ file: BusSt Science student’s file: SciSt –BusSt U SciSt: –BusSt ∩ SciSt –BusSt – SciSt Spring 06 Student file: S06St Fall 06 Student file: F06St –S06St – F06St –F06St – S06St

Product Set1 = {a, b, c} Set2 = {X, Y, Z} Set1 X Set2 = {aX, aY aZ, bX, bY, bZ, cX, cY, cZ}

Faculty File: FIDFname F1Chao F2Smith Student File: SIDSname FID S1PeterF1 S2PaulF2 S3SmithF1 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, SnameSexMajor S1PeterMBus S2PaulMArt S3MaryFBus S4NancyFSci S5PeterMArt π sid, sname (Student) π sname, sex (Student) π sname, sex ( σ Major = ‘Bus’ (Student)) –Does not equal to: σ Major = ‘Bus’ ( π sname, sex (Student))

Duplications due to Projection WorkLog file: EIDPjIDHours E1P25 E1P14 E2P26 E2P18 E3P14 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: FIDFname F1Chao F2Smith Student File: SIDSname FID S1PeterF1 S2PaulF2 S3SmithF1 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, Phone –Course: CID, Cname, Credits, FID –StudentCourse: SID, CID

Questions Q1: Display College of Business students’ ID and name. Q2: Display students’ ID and name who owe university more than $2000. Q3: Display faculty’s name and phone if the student’s GPA is lower than 2.0. Q4: Display faculty’s name and phone if the faculty advises at least one student. Q5: Display faculty’s name and phone if the faculty does not advise any student. Q6: Display students’ ID and name who are taking at least one course. Q7: Display students’ ID and name who do not take any course. Q8: Display students’ ID and name who are taking 464 and GPA < 2.0 Q9: Display students’ ID and name who are taking Chao’s courses. Q10: Display students’ ID and name who are taking 464 and 363.