2 rel-algebra

Relational Model & Algebra Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems November 9, 2011 Some slide content courtesy of Susan Davidson & Raghu Ramakrishnan

Recall Our Initial Discussion… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Relational Data Model (1970) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Why Did It Take So Many Years to Implement Relational Databases? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Getting More Concrete: Building a Database and Application ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Conceptual Design for CIS Student Course Survey STUDENT COURSE Takes name sid cid name PROFESSOR Teaches semester fid name exp-grade “ Who’s taking what, and what grade do they expect?” This design is independent of the final form of the report!

Example Schema ,[object Object],[object Object],STUDENT Takes COURSE PROFESSOR Teaches sid name 1 Jill 2 Qun 3 Nitin fid name 1 Ives 2 Taskar 8 Martin sid exp-grade cid 1 A 550-0109 1 A 520-1009 3 C 500-0109 cid subj sem 550-0109 DB F09 520-1009 AI S09 501-0109 Arch F09 fid cid 1 550-0109 2 520-1009 8 501-0109

Some Terminology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Describing Relations ,[object Object],[object Object],[object Object],STUDENT (sid:int, name:string) Takes (sid:int, exp-grade:char[2], cid:string) COURSE (cid:string, subj:string, sem:char[3]) Teaches (fid:int, cid:string) PROFESSOR (fid:int, name:string)

More on Attribute Domains ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Integrity Constraints ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

SQL: Structured Query Language ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Table Definition: SQL-92 DDL and Constraints CREATE TABLE Takes (sid INTEGER, exp-grade CHAR(2), cid STRING(8), PRIMARY KEY (sid, cid), FOREIGN KEY (sid) REFERENCES STUDENT, FOREIGN KEY (cid) REFERENCES COURSE ) CREATE TABLE STUDENT (sid INTEGER, name CHAR(20), )

Example Data Instance STUDENT Takes COURSE PROFESSOR Teaches sid name 1 Jill 2 Qun 3 Nitin fid name 1 Ives 2 Taskar 8 Martin sid exp-grade cid 1 A 550-0109 1 A 520-1009 3 C 501-0109 cid subj sem 550-0109 DB F09 520-1009 AI S09 501-0109 Arch F09 fid cid 1 550-0109 2 700-1009 8 501-0109

From Tables  SQL  Web Application ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],C -> machine code sequence -> microprocessor Java -> bytecode sequence -> JVM SQL -> relational algebra expression -> query execution engine

Codd’s Relational Algebra ,[object Object],[object Object],[object Object]

Codd’s Logical Operations: The Relational Algebra ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Data Instance for Operator Examples STUDENT Takes COURSE PROFESSOR Teaches sid name 1 Jill 2 Qun 3 Nitin 4 Marty fid name 1 Ives 2 Taskar 8 Martin sid exp-grade cid 1 A 550-0109 1 A 520-1009 3 A 520-1009 3 C 501-0109 4 C 501-0109 cid subj sem 550-0109 DB F09 520-1009 AI S09 501-0109 Arch F09 fid cid 1 550-0109 2 520-1009 8 501-0109

Join, ⋈  : A Combination of Product and Selection

Rename,     ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Mini-Quiz ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Deriving Intersection ,[object Object],A-B B-A A B A Å B ≡ (A [ B) – (A – B) – (B – A) ≡ (A – B) – (B – A)

Division ,[object Object],[object Object],[object Object]

Division: R 1  R 2 ,[object Object],[object Object],[object Object],[object Object], fid (  fid,subj ( Teaches ⋈ COURSE)   subj (COURSE))

Division Using Our Existing Operators ,[object Object],[object Object],[object Object], fid,subj (PROFESSOR £  subj (COURSE)) Allpairs -  fid,subj (Teaches ⋈ COURSE)  fid (PROFESSOR) -  fid (NotTaught) ´  fid (PROFESSOR) -  fid (  fid,subj (PROFESSOR £  subj (COURSE)) -  fid,subj (Teaches ⋈ COURSE))

The Big Picture: SQL to Algebra to Query Plan to Web Page SELECT * FROM STUDENT, Takes, COURSE WHERE STUDENT.sid = Takes.sID AND Takes.cID = cid Optimizer Execution Engine Storage Subsystem Web Server / UI / etc Query Plan – an operator tree STUDENT Takes COURSE Merge Hash by cid by cid

Hint of Future Things: Optimization Is Based on Algebraic Equivalences ,[object Object],[object Object], c Ç d (R) ´  c (R) [  d (R)  c (R 1 £ R 2 ) ´ R 1 ⋈ c R 2  c Ç d (R) ´  c (  d (R)) ,[object Object]

Next Time: An Equivalent, But Very Different, Formalism ,[object Object],[object Object],[object Object],[object Object]

2 rel-algebra

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