1. Carnegie Mellon Carnegie Mellon Univ. Dept. of Computer Science 15-415 - Database Applications C. Faloutsos Relational model

2. Carnegie Mellon 15-415 - C. Faloutsos2 Overview history concepts Formal query languages –relational algebra –rel. tuple calculus –rel. domain calculus

3. Carnegie Mellon 15-415 - C. Faloutsos3 History before: records, pointers, sets etc introduced by E.F. Codd in 1970 revolutionary! first systems: 1977-8 (System R; Ingres) Turing award in 1981

4. Carnegie Mellon 15-415 - C. Faloutsos4 Concepts Database: a set of relations (= tables) rows: tuples columns: attributes (or keys) superkey, candidate key, primary key

5. Carnegie Mellon 15-415 - C. Faloutsos5 Example Database:

6. Carnegie Mellon 15-415 - C. Faloutsos6 Example: cont’d Database: rel. schema (attr+domains) tuple k-th attribute (Dk domain)

7. Carnegie Mellon 15-415 - C. Faloutsos7 Example: cont’d rel. schema (attr+domains) instance

8. Carnegie Mellon 15-415 - C. Faloutsos8 Example: cont’d rel. schema (attr+domains) instance Di: the domain of the I-th attribute (eg., char(10) Formally: an instance is a subset of (D1 x D2 x …x Dn)

9. Carnegie Mellon 15-415 - C. Faloutsos9 Example: cont’d superkey (eg., ‘ssn, name’): determines record cand. key (eg., ‘ssn’, or ‘st#’): minimal superkey primary key: one of the cand. keys

10. Carnegie Mellon 15-415 - C. Faloutsos10 Overview history concepts Formal query languages –relational algebra –rel. tuple calculus –rel. domain calculus

11. Carnegie Mellon 15-415 - C. Faloutsos11 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?

12. Carnegie Mellon 15-415 - C. Faloutsos12. set union U set difference ‘-’ Relational operators

13. Carnegie Mellon 15-415 - C. Faloutsos13 Example: Q: find all students (part or full time) A: PT-STUDENT union FT-STUDENT

14. Carnegie Mellon 15-415 - C. Faloutsos14 Observations: two tables are ‘union compatible’ if they have the same attributes (‘domains’) Q: how about intersection U

15. Carnegie Mellon 15-415 - C. Faloutsos15 Observations: A: redundant: STUDENT intersection STAFF = STUDENT - (STUDENT - STAFF) STUDENT STAFF

16. Carnegie Mellon 15-415 - C. Faloutsos16. set union set difference ‘-’ Relational operators U

17. Carnegie Mellon 15-415 - C. Faloutsos17 Other operators? eg, find all students on ‘Main street’ A: ‘selection’

18. Carnegie Mellon 15-415 - C. Faloutsos18 Other operators? Notice: selection (and rest of operators) expect tables, and produce tables (-> can be cascaded!!) For selection, in general:

19. Carnegie Mellon 15-415 - C. Faloutsos19 Selection - examples Find all ‘Smiths’ on ‘Forbes Ave’ ‘condition’ can be any boolean combination of ‘=‘, ‘>’, ‘>=‘,...

20. Carnegie Mellon 15-415 - C. Faloutsos20 selection. set union set difference R - S Relational operators R U S

21. Carnegie Mellon 15-415 - C. Faloutsos21 selection picks rows - how about columns? A: ‘projection’ - eg.: finds all the ‘ssn’ - removing duplicates Relational operators

22. Carnegie Mellon 15-415 - C. Faloutsos22 Cascading: ‘find ssn of students on ‘forbes ave’ Relational operators

23. Carnegie Mellon 15-415 - C. Faloutsos23 selection projection. set union set difference R - S Relational operators R U S

24. Carnegie Mellon 15-415 - C. Faloutsos24 Are we done yet? Q: Give a query we can not answer yet! Relational operators

25. Carnegie Mellon 15-415 - C. Faloutsos25 A: any query across two or more tables, eg., ‘find names of students in 15-415’ Q: what extra operator do we need?? A: surprisingly, cartesian product is enough! Relational operators

26. Carnegie Mellon 15-415 - C. Faloutsos26 Cartesian product eg., dog-breeding: MALE x FEMALE gives all possible couples x =

27. Carnegie Mellon 15-415 - C. Faloutsos27 so what? Eg., how do we find names of students taking 415?

28. Carnegie Mellon 15-415 - C. Faloutsos28 Cartesian product A:

29. Carnegie Mellon 15-415 - C. Faloutsos29 Cartesian product

30. Carnegie Mellon 15-415 - C. Faloutsos30

31. Carnegie Mellon 15-415 - C. Faloutsos31 selection projection cartesian product MALE x FEMALE set union set difference R - S FUNDAMENTAL Relational operators R U S

32. Carnegie Mellon 15-415 - C. Faloutsos32 Relational ops Surprisingly, they are enough, to help us answer almost any query we want!! derived operators, for convenience –set intersection –join (theta join, equi-join, natural join) –‘rename’ operator –division

33. Carnegie Mellon 15-415 - C. Faloutsos33 Joins Equijoin:

34. Carnegie Mellon 15-415 - C. Faloutsos34 Cartesian product A:

35. Carnegie Mellon 15-415 - C. Faloutsos35 Joins Equijoin: theta-joins: generalization of equi-join - any condition

36. Carnegie Mellon 15-415 - C. Faloutsos36 Joins very popular: natural join: R S like equi-join, but it drops duplicate columns: STUDENT(ssn, name, address) TAKES(ssn, cid, grade)

37. Carnegie Mellon 15-415 - C. Faloutsos37 Joins nat. join has 5 attributes equi-join: 6

38. Carnegie Mellon 15-415 - C. Faloutsos38 Natural Joins - nit-picking if no attributes in common between R, S: nat. join -> cartesian product:

39. Carnegie Mellon 15-415 - C. Faloutsos39 Overview - rel. algebra fundamental operators derived operators –joins etc –rename –division examples

40. Carnegie Mellon 15-415 - C. Faloutsos40 rename op. Q: why? A: shorthand; self-joins; … for example, find the grand-parents of ‘Tom’, given PC(parent-id, child-id)

41. Carnegie Mellon 15-415 - C. Faloutsos41 rename op. PC(parent-id, child-id)

42. Carnegie Mellon 15-415 - C. Faloutsos42 rename op. first, WRONG attempt: (why? how many columns?) Second WRONG attempt:

43. Carnegie Mellon 15-415 - C. Faloutsos43 rename op. we clearly need two different names for the same table - hence, the ‘rename’ op.

44. Carnegie Mellon 15-415 - C. Faloutsos44 Overview - rel. algebra fundamental operators derived operators –joins etc –rename –division examples

45. Carnegie Mellon 15-415 - C. Faloutsos45 Division Rarely used, but powerful. Example: find suspicious suppliers, ie., suppliers that supplied all the parts in A_BOMB

46. Carnegie Mellon 15-415 - C. Faloutsos46 Division

47. Carnegie Mellon 15-415 - C. Faloutsos47 Division Observations: ~reverse of cartesian product It can be derived from the 5 fundamental operators (!!) How?

48. Carnegie Mellon 15-415 - C. Faloutsos48 Division Answer:

49. Carnegie Mellon 15-415 - C. Faloutsos49 Overview - rel. algebra fundamental operators derived operators –joins etc –rename –division examples

50. Carnegie Mellon 15-415 - C. Faloutsos50 Sample schema find names of students that take 15-415

51. Carnegie Mellon 15-415 - C. Faloutsos51 Examples find names of students that take 15-415

52. Carnegie Mellon 15-415 - C. Faloutsos52 Sample schema find course names of ‘smith’

53. Carnegie Mellon 15-415 - C. Faloutsos53 Examples find course names of ‘smith’

54. Carnegie Mellon 15-415 - C. Faloutsos54 Examples find ssn of ‘overworked’ students, ie., that take 412, 413, 415

55. Carnegie Mellon 15-415 - C. Faloutsos55 Examples find ssn of ‘overworked’ students, ie., that take 412, 413, 415: almost correct answer: U U U

56. Carnegie Mellon 15-415 - C. Faloutsos56 Examples find ssn of ‘overworked’ students, ie., that take 412, 413, 415 - Correct answer: U U U c-name=413 c-name=415

57. Carnegie Mellon 15-415 - C. Faloutsos57 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

58. Carnegie Mellon 15-415 - C. Faloutsos58 Sample schema

59. Carnegie Mellon 15-415 - C. Faloutsos59 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

60. Carnegie Mellon 15-415 - C. Faloutsos60 Conclusions Relational model: only tables (‘relations’) relational algebra: powerful, minimal: 5 operators can handle almost any query! most non-trivial op.: join