Relational Algebra Equivalencies. Database Systems: The Complete Book Ch

Transcription

1 elational Algebra Equivalencies Database ystems: he Complete Book Ch

2 Implementing: Joins olution 1 (Nested-Loop) For Each (a in A) { For Each (b in B) { emit (a, b); }} A B 2

3 Implementing: Joins olution 1 (Nested-Loop) For Each (a in A) { For Each (b in B) { emit (a, b); }} A B 2

4 Implementing: Joins olution 2 (Block-Nested-Loop) 3

5 Implementing: Joins 1) Partition into Blocks olution 2 (Block-Nested-Loop) 4

6 Implementing: Joins olution 2 (Block-Nested-Loop) 1) Partition into Blocks 2) NLJ on each pair of blocks 4

7 Implementing: Joins olution 3 (ort-merge Join) Keep iterating on the set with the lowest value. When you hit two that match, emit, then iterate both A B 5

8 Implementing: Joins olution 3 (ort-merge Join) Keep iterating on the set with the lowest value. When you hit two that match, emit, then iterate both A B 5

9 Implementing: Joins olution 3 (ort-merge Join) Keep iterating on the set with the lowest value. When you hit two that match, emit, then iterate both A B 5

10 Implementing: Joins olution 3 (ort-merge Join) Keep iterating on the set with the lowest value. When you hit two that match, emit, then iterate both A B 5

11 Implementing: Joins olution 3 (ort-merge Join) Keep iterating on the set with the lowest value. When you hit two that match, emit, then iterate both A B 5

12 Implementing: Joins olution 3 (ort-merge Join) Keep iterating on the set with the lowest value. When you hit two that match, emit, then iterate both A Done! B 5

13 Implementing: Joins olution 4 (Eternal Hash) A B 6

14 Implementing: Joins olution 4 (Eternal Hash) 1) Build a hash table on both relations A B 6

15 Implementing: Joins olution 4 (Eternal Hash) 1) Build a hash table on both relations 2) In-Memory Nested-Loop Join on each hash bucket (subdivide buckets using a different hash fn if needed) A B 1 5 6

16 (Essentially a more efficient 7 nested loop join) Implementing: Joins olution 5 (Grace/Hybrid Hash) Keep the hash table in memory A B

17 (Essentially a more efficient 7 nested loop join) Implementing: Joins olution 5 (Grace/Hybrid Hash) Keep the hash table in memory A 5 B

18 Implementing: Joins olution 5 (Grace/Hybrid Hash) Keep the hash table in memory A 5 B 1 5 (Essentially a more efficient 7 nested loop join)

19 Implementing: Joins olution 6 (Inde-Nested-Loop) Like nested-loop, but use an inde to make the inner loop much faster! 8

20 Implementing: Joins olution 6 (Inde-Nested-Loop) Like nested-loop, but use an inde to make the inner loop much faster! 8

21 Implementing: Joins olution 6 (Inde-Nested-Loop) Like nested-loop, but use an inde to make the inner loop much faster! 8

22 Implementing: Joins olution 6 (Inde-Nested-Loop) Like nested-loop, but use an inde to make the inner loop much faster! 8

23 Implementing: Joins olution 6 (Inde-Nested-Loop) Like nested-loop, but use an inde to make the inner loop much faster! 8

24 Implementing: Joins olution 6 (Inde-Nested-Loop) Like nested-loop, but use an inde to make the inner loop much faster! 8

25 What are the tradeoffs of each algorithm? What properties do we care about? How do the algorithms compare? 9

26 Implementing: Joins radeoffs Nested Loop Pipelined? 1/2 Memory equirements? 1 able Predicate Limitation? No Block-Nested Loop No 2 Blocks No Inde-Nested Loop 1/2 1 uple (+Inde) ingle Comparison ort-merge Hash If Data orted No ame as reqs. of orting Inputs Ma of 1 Page per Bucket and All Pages in Any Bucket Equality Only Equality Only Grace Hash 1/2 Hash able Equality Only 10

27 .sql elect Createable aved chema π σ Iterator PLAYE.dat (Output)

28 .sql elect Createable aved chema Optimizer π σ Iterator PLAYE.dat (Output)

29 Equivalent Epressions hey look the same, but one is good, one is evil (No Beard) (Beard) (Leonard Nimoy) = (Zachary Quinto) wo different epressions of the same character

30 Query Optimization If X and Y are equivalent and Y is better then replace all Xs with Ys

31 Equivalent Epressions < A > < 1 > < 2 > < 2 > < A, B > < 2, 4 > < 3, 5 > < 3, 6 >

32 Equivalent Epressions < A > < 1 > < 2 > < 2 > < A, B > < 2, 4 > < 3, 5 > < 3, 6 > Is?

33 Equivalent Epressions < A > < 1 > < 2 > < 2 > < A, B > < 2, 4 > < 3, 5 > < 3, 6 > Is? Is?

34 Equivalent Epressions < A > < 1 > < 2 > < 2 > < A, B > < 2, 4 > < 3, 5 > < 3, 6 > Is? Is? Is?

35 Equivalent Epressions < A > < 1 > < 2 > < 2 > < A, B > < 2, 4 > < 3, 5 > < 3, 6 > Is? Is? Is? Is?

36 Equivalent Epressions wo epressions are equivalent if they produce the same output

37 Equivalent Epressions wo epressions are equivalent if they produce the same output but

38 Equivalent Epressions < A > < 1 > < 2 > < 2 > < A > =? < 2 > < 1 > =? < 2 > < A > < 1 > < 2 > Equivalence under - Bag emantics: he same tuples (order-independent) - et emantics: he same set of tuples (count-independent) - List emantics: he same tuples (order matters)

39 Equivalent Epressions < A > < 1 > < 2 > < 2 > < A > =? < 2 > < 1 > =? < 2 > < A > < 1 > < 2 > Equivalence under - Bag emantics: he same tuples (order-independent) - et emantics: he same set of tuples (count-independent) - List emantics: he same tuples (order matters)

40 A Equivalencies election Projection Cross Product (and Join) (Decomposable) (Decomposable) (Commutative) (Idempotent) (Associative) (Commutative) ry It: how that

41 election and Projection election commutes with Projection (but only if attribute set a and condition c are compatible) a must include all columns referenced by c how that

42 election and Projection election commutes with Projection (but only if attribute set a and condition c are compatible) a must include all columns referenced by c how that When is this rewrite a good idea?

43 Join election combines with Cross Product to form a Join as per the definition of Join (Note: his only helps if we have a join algorithm for conditions like c) how that

44 Join election combines with Cross Product to form a Join as per the definition of Join (Note: his only helps if we have a join algorithm for conditions like c) how that When is this rewrite a good idea?

45 election and Cross Product election commutes with Cross Product (but only if condition c references attributes of eclusively) how that

46 election and Cross Product election commutes with Cross Product (but only if condition c references attributes of eclusively) how that When is this rewrite a good idea?

47 Projection and Cross Product Projection commutes (distributes) over Cross Product (where a1 and a2 are the attributes in a from and respectively) how that (under what condition) How can we work around this limitation?

48 Projection and Cross Product Projection commutes (distributes) over Cross Product (where a1 and a2 are the attributes in a from and respectively) how that (under what condition) How can we work around this limitation? When is this rewrite a good idea?

49 A Equivalencies Union and Intersections are Commutative and Associative election and Projection both commute with both Union and Intersection

50 A Equivalencies Union and Intersections are Commutative and Associative election and Projection both commute with both Union and Intersection When is this rewrite a good idea?

51 Eample ELEC.A,.E FOM,, WHEE.B =.B AND.C < 5 AND.D =.D

52 Eample

53 Eample

54 Eample

55 Eample

56 Eample

57 Eample

58 Eample

59 Eample

60 Eample

61 Eample

62 Eample

63 Eample

64 Eample

65 Eample

66 Eample

67 Eample

68 Eample

69 Eample

70 Final Plan ELEC.A,.E FOM,, WHEE.B =.B AND.C < 5 AND.D =.D

71 ranslate Dumb, Optimize Later Find Patterns (elect(cross(,))) and eplace (Join(,))

72 A Equivalencies (./ )./ vs./ (./ )

73 A Equivalencies (./ )./ vs./ (./ ) Which form is better?