Faloutsos - Pavlo CMU SCS /615

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1 Faloutsos - Pavlo /615 Carnegie Mellon Univ. School of Computer Science /615 - DB Applications C. Faloutsos & A. Pavlo Lecture #4: Relational Algebra Overview history concepts Formal query languages relational algebra rel. tuple calculus rel. domain calculus Faloutsos - Pavlo /615 #2 History before: records, pointers, sets etc introduced by E.F. Codd in 1970 revolutionary! first systems: (System R; Ingres) Turing award in 1981 Faloutsos - Pavlo /615 #3 1

2 Faloutsos - Pavlo /615 Concepts - reminder Database: a set of relations (= tables) rows: tuples columns: attributes (or keys) superkey, candidate key, primary key Faloutsos - Pavlo /615 #4 Database: Example Faloutsos - Pavlo /615 #5 Example: cont d Database: k-th attribute (Dk domain) rel. schema (attr+domains) tuple Faloutsos - Pavlo /615 #6 2

3 Faloutsos - Pavlo /615 Example: cont d rel. schema (attr+domains) instance Faloutsos - Pavlo /615 #7 Example: cont d Di: the domain of the i-th attribute (eg., char(10) rel. schema (attr+domains) instance Faloutsos - Pavlo /615 #8 Overview history concepts Formal query languages relational algebra rel. tuple calculus rel. domain calculus Faloutsos - Pavlo /615 #9 3

4 Faloutsos - Pavlo /615 Formal query languages How do we collect information? Eg., find ssn s of people in 415 (recall: everything is a set!) One solution: Rel. algebra, ie., set operators Q1: Which ones?? Q2: what is a minimal set of operators? Faloutsos - Pavlo /615 #10... Relational operators set union U set difference - Faloutsos - Pavlo /615 #11 Example: Q: find all students (part or full time) A: PT-STUDENT union FT-STUDENT Faloutsos - Pavlo /615 #12 4

5 Faloutsos - Pavlo /615 Observations: two tables are union compatible if they have the same attributes ( domains ) Q: how about intersection U Faloutsos - Pavlo /615 #13 Observations: A: redundant: STUDENT intersection STAFF = STUDENT STAFF Faloutsos - Pavlo /615 #14 Observations: A: redundant: STUDENT intersection STAFF = STUDENT STAFF Faloutsos - Pavlo /615 #15 5

6 Faloutsos - Pavlo /615 Observations: A: redundant: STUDENT intersection STAFF = STUDENT - (STUDENT - STAFF) STUDENT STAFF Faloutsos - Pavlo /615 #16 Observations: A: redundant: STUDENT intersection STAFF = STUDENT - (STUDENT - STAFF) Double negation: We ll see it again, later Faloutsos - Pavlo /615 #17... Relational operators set union U set difference - Faloutsos - Pavlo /615 #18 6

7 Faloutsos - Pavlo /615 Other operators? eg, find all students on Main street A: selection Faloutsos - Pavlo /615 #19 Other operators? Notice: selection (and rest of operators) expect tables, and produce tables (-> can be cascaded!!) For selection, in general: Faloutsos - Pavlo /615 #20 Selection - examples Find all Smiths on Forbes Ave condition can be any boolean combination of =, >, >=,... Faloutsos - Pavlo /615 #21 7

8 Faloutsos - Pavlo /615 Relational operators selection.. set union set difference R U S R - S Faloutsos - Pavlo /615 #22 Relational operators selection picks rows - how about columns? A: projection - eg.: finds all the ssn - removing duplicates Faloutsos - Pavlo /615 #23 Relational operators Cascading: find ssn of students on forbes ave Faloutsos - Pavlo /615 #24 8

9 Faloutsos - Pavlo /615 Relational operators selection projection. set union set difference R U S R - S Faloutsos - Pavlo /615 #25 Relational operators Are we done yet? Q: Give a query we can not answer yet! Faloutsos - Pavlo /615 #26 Relational operators A: any query across two or more tables, eg., find names of students in Q: what extra operator do we need?? Faloutsos - Pavlo /615 #27 9

10 Faloutsos - Pavlo /615 Relational operators A: any query across two or more tables, eg., find names of students in Q: what extra operator do we need?? A: surprisingly, cartesian product is enough! Faloutsos - Pavlo /615 #28 Cartesian product eg., dog-breeding: MALE x FEMALE gives all possible couples x = Faloutsos - Pavlo /615 #29 so what? Eg., how do we find names of students taking 415? Faloutsos - Pavlo /615 #30 10

11 Faloutsos - Pavlo /615 A: Cartesian product Faloutsos - Pavlo /615 #31 Cartesian product Faloutsos - Pavlo /615 #32 Faloutsos - Pavlo /615 #33 11

12 Faloutsos - Pavlo /615 FUNDAMENTAL Relational operators selection projection cartesian product set union set difference MALE x FEMALE R U S R - S Faloutsos - Pavlo /615 #34 Relational ops Surprisingly, they are enough, to help us answer almost any query we want!! derived/convenience operators: set intersection join (theta join, equi-join, natural join) rename operator division Faloutsos - Pavlo /615 #35 Equijoin: Joins Faloutsos - Pavlo /615 #36 12

13 Faloutsos - Pavlo /615 Cartesian product A: Faloutsos - Pavlo /615 #37 Joins Equijoin: theta-joins: generalization of equi-join - any condition Faloutsos - Pavlo /615 #38 Joins very popular: natural join: R S like equi-join, but it drops duplicate columns: STUDENT (ssn, name, address) TAKES (ssn, cid, grade) Faloutsos - Pavlo /615 #39 13

14 Faloutsos - Pavlo /615 Joins nat. join has 5 attributes equi-join: 6 Faloutsos - Pavlo /615 #40 Natural Joins - nit-picking if no attributes in common between R, S: nat. join -> cartesian product Faloutsos - Pavlo /615 #41 Overview - rel. algebra fundamental operators derived operators joins etc rename division examples Faloutsos - Pavlo /615 #42 14

15 Faloutsos - Pavlo /615 Rename op. Q: why? A: shorthand; self-joins; for example, find the grand-parents of Tom, given PC (parent-id, child-id) Faloutsos - Pavlo /615 #43 Rename op. PC (parent-id, child-id) Faloutsos - Pavlo /615 #44 Rename op. first, WRONG attempt: (why? how many columns?) Second WRONG attempt: Faloutsos - Pavlo /615 #45 15

16 Faloutsos - Pavlo /615 Rename op. we clearly need two different names for the same table - hence, the rename op. Faloutsos - Pavlo /615 #46 Overview - rel. algebra fundamental operators derived operators joins etc rename division examples Faloutsos - Pavlo /615 #47 Division Rarely used, but powerful. Example: find suspicious suppliers, ie., suppliers that supplied all the parts in A_BOMB Faloutsos - Pavlo /615 #48 16

17 Faloutsos - Pavlo /615 Division Faloutsos - Pavlo /615 #49 Division Observations: ~reverse of cartesian product It can be derived from the 5 fundamental operators (!!) How? Faloutsos - Pavlo /615 #50 Answer: Division Observation: find good suppliers, and subtract! (double negation) Faloutsos - Pavlo /615 #51 17

18 Faloutsos - Pavlo /615 Answer: Division Observation: find good suppliers, and subtract! (double negation) Faloutsos - Pavlo /615 #52 Answer: Division All suppliers All bad parts Faloutsos - Pavlo /615 #53 Answer: Division all possible suspicious shipments Faloutsos - Pavlo /615 #54 18

19 Faloutsos - Pavlo /615 Answer: Division all possible suspicious shipments that didn t happen Faloutsos - Pavlo /615 #55 Answer: Division all suppliers who missed at least one suspicious shipment, i.e.: good suppliers Faloutsos - Pavlo /615 #56 Overview - rel. algebra fundamental operators derived operators joins etc rename division examples Faloutsos - Pavlo /615 #57 19

20 Faloutsos - Pavlo /615 Sample schema find names of students that take Faloutsos - Pavlo /615 #58 Examples find names of students that take Faloutsos - Pavlo /615 #59 Examples find names of students that take Faloutsos - Pavlo /615 #60 20

21 Faloutsos - Pavlo /615 find course names of smith Sample schema Faloutsos - Pavlo /615 #61 Examples find course names of smith Faloutsos - Pavlo /615 #62 Examples find ssn of overworked students, ie., that take 412, 413, 415 Faloutsos - Pavlo /615 #63 21

22 Faloutsos - Pavlo /615 Examples find ssn of overworked students, ie., that take 412, 413, 415: almost correct answer: Faloutsos - Pavlo /615 #64 Examples find ssn of overworked students, ie., that take 412, 413, Correct answer: c-name=413 c-name=415 Faloutsos - Pavlo /615 #65 Examples find ssn of students that work at least as hard as ssn=123, ie., they take all the courses of ssn=123, and maybe more Faloutsos - Pavlo /615 #66 22

23 Faloutsos - Pavlo /615 Sample schema Faloutsos - Pavlo /615 #67 Examples find ssn of students that work at least as hard as ssn=123 (ie., they take all the courses of ssn=123, and maybe more Faloutsos - Pavlo /615 #68 Conclusions Relational model: only tables ( relations ) relational algebra: powerful, minimal: 5 operators can handle almost any query! Faloutsos - Pavlo /615 #69 23