1. CMU SCS Carnegie Mellon Univ. School of Computer Science 15-415/615 - DB Applications C. Faloutsos & A. Pavlo Lecture #4: Relational Algebra

2. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#2 Overview history concepts Formal query languages –relational algebra –rel. tuple calculus –rel. domain calculus

3. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#3 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. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#4 Concepts - reminder Database: a set of relations (= tables) rows: tuples columns: attributes (or keys) superkey, candidate key, primary key

5. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#5 Example Database:

6. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#6 Example: cont’d Database: rel. schema (attr+domains) tuple k-th attribute (Dk domain)

7. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#7 Example: cont’d rel. schema (attr+domains) instance

8. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#8 Example: cont’d rel. schema (attr+domains) instance Di: the domain of the i-th attribute (eg., char(10)

9. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#9 Overview history concepts Formal query languages –relational algebra –rel. tuple calculus –rel. domain calculus

10. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#10 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?

11. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#11. set union U set difference ‘-’ Relational operators

12. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#12 Example: Q: find all students (part or full time) A: PT-STUDENT union FT-STUDENT

13. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#13 Observations: two tables are ‘union compatible’ if they have the same attributes (‘domains’) Q: how about intersection U

14. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#14 Observations: A: redundant: STUDENT intersection STAFF = STUDENT STAFF

15. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#15 Observations: A: redundant: STUDENT intersection STAFF = STUDENT STAFF

16. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#16 Observations: A: redundant: STUDENT intersection STAFF = STUDENT - (STUDENT - STAFF) STUDENT STAFF

17. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#17 Observations: A: redundant: STUDENT intersection STAFF = STUDENT - (STUDENT - STAFF) Double negation: We’ll see it again, later…

18. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#18. set union set difference ‘-’ Relational operators U

19. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#19 Other operators? eg, find all students on ‘Main street’ A: ‘selection’

20. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#20 Other operators? Notice: selection (and rest of operators) expect tables, and produce tables (-> can be cascaded!!) For selection, in general:

21. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#21 Selection - examples Find all ‘Smiths’ on ‘Forbes Ave’ ‘condition’ can be any boolean combination of ‘=‘, ‘>’, ‘>=‘,...

22. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#22 selection. set union set difference R - S Relational operators R U S

23. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#23 selection picks rows - how about columns? A: ‘projection’ - eg.: finds all the ‘ssn’ - removing duplicates Relational operators

24. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#24 Cascading: ‘find ssn of students on ‘forbes ave’ Relational operators

25. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#25 selection projection. set union set difference R - S Relational operators R U S

26. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#26 Are we done yet? Q: Give a query we can not answer yet! Relational operators

27. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#27 A: any query across two or more tables, eg., ‘find names of students in 15-415’ Q: what extra operator do we need?? Relational operators

28. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#28 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

29. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#29 Cartesian product eg., dog-breeding: MALE x FEMALE gives all possible couples x =

30. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#30 so what? Eg., how do we find names of students taking 415?

31. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#31 Cartesian product A:

32. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#32 Cartesian product

33. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#33

34. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#34 selection projection cartesian product MALE x FEMALE set union set difference R - S FUNDAMENTAL Relational operators R U S

35. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#35 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

36. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#36 Joins Equijoin:

37. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#37 Cartesian product A:

38. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#38 Joins Equijoin: theta-joins: generalization of equi-join - any condition

39. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#39 Joins very popular: natural join: R S like equi-join, but it drops duplicate columns: STUDENT (ssn, name, address) TAKES (ssn, cid, grade)

40. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#40 Joins nat. join has 5 attributes equi-join: 6

41. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#41 Natural Joins - nit-picking if no attributes in common between R, S: nat. join -> cartesian product

42. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#42 Overview - rel. algebra fundamental operators derived operators –joins etc –rename –division examples

43. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#43 Rename op. Q: why? A: shorthand; self-joins; … for example, find the grand-parents of ‘Tom’, given PC (parent-id, child-id)

44. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#44 Rename op. PC (parent-id, child-id)

45. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#45 Rename op. first, WRONG attempt: (why? how many columns?) Second WRONG attempt:

46. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#46 Rename op. we clearly need two different names for the same table - hence, the ‘rename’ op.

47. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#47 Overview - rel. algebra fundamental operators derived operators –joins etc –rename –division examples

48. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#48 Division Rarely used, but powerful. Example: find suspicious suppliers, ie., suppliers that supplied all the parts in A_BOMB

49. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#49 Division

50. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#50 Division Observations: ~reverse of cartesian product It can be derived from the 5 fundamental operators (!!) How?

51. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#51 Division Answer: Observation: find ‘good’ suppliers, and subtract! (double negation)

52. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#52 Division Answer: Observation: find ‘good’ suppliers, and subtract! (double negation)

53. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#53 Division Answer: All suppliers All bad parts

54. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#54 Division Answer: all possible suspicious shipments

55. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#55 Division Answer: all possible suspicious shipments that didn’t happen

56. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#56 Division Answer: all suppliers who missed at least one suspicious shipment, i.e.: ‘good’ suppliers

57. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#57 Overview - rel. algebra fundamental operators derived operators –joins etc –rename –division examples

58. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#58 Sample schema find names of students that take 15-415

59. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#59 Examples find names of students that take 15-415

60. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#60 Examples find names of students that take 15-415

61. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#61 Sample schema find course names of ‘smith’

62. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#62 Examples find course names of ‘smith’

63. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#63 Examples find ssn of ‘overworked’ students, ie., that take 412, 413, 415

64. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#64 Examples find ssn of ‘overworked’ students, ie., that take 412, 413, 415: almost correct answer:

65. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#65 Examples find ssn of ‘overworked’ students, ie., that take 412, 413, 415 - Correct answer: c-name=413 c-name=415

66. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#66 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

67. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#67 Sample schema

68. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#68 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

69. CMU SCS Faloutsos - PavloCMU SCS 15-415/615#69 Conclusions Relational model: only tables (‘relations’) relational algebra: powerful, minimal: 5 operators can handle almost any query!