1. CS 4432logical query rewriting - lecture 151 CS4432: Database Systems II Lecture #15 Logical Query Rewriting Professor Elke A. Rundensteiner

2. CS 4432logical query rewriting - lecture 152 Query in SQL  Query Plan in Algebra (logical)  Other Query Plan in Algebra (logical)

3. CS 4432logical query rewriting - lecture 153 Query plan 1 (in relational algebra)  B,D  R.A =“c”  S.E=2  R.C=S.C  X RS

4. CS 4432logical query rewriting - lecture 154 Query plan 2 (in relational algebra)  B,D  R.A = “c”  S.E = 2 R S natural join on R.C=S.C

5. CS 4432logical query rewriting - lecture 155 Relational algebra optimization What are transformation rules ? –preserve equivalence What are good transformations? –reduce query execution costs

6. CS 4432logical query rewriting - lecture 156 Rules: Natural join rewriting. R S=SR (R S) T= R (S T) R SS T T R Can also write as trees, e.g.:

7. CS 4432logical query rewriting - lecture 157 Rules: Other binary operators ? R S=SR (R S) T= R (S T) What about : Cross product? Condition join? Union? Intersection ? Difference ?

8. CS 4432logical query rewriting - lecture 158 Note: Carry attribute names in results, so order is not important T R R SS T

9. CS 4432logical query rewriting - lecture 159 R x S = S x R (R x S) x T = R x (S x T) R U S = S U R R U (S U T) = (R U S) U T Rules: Natural joins & cross products & union R S=SR (R S) T= R (S T)

10. CS 4432logical query rewriting - lecture 1510 Rules: Selects  p1  p2 (R)=  p1 [  p2 (R)] [  p1 (R)] U [  p2 (R)]  p1vp2 (R) =

11. CS 4432logical query rewriting - lecture 1511 Bags vs. Sets R = {a,a,b,b,b,c} S = {b,b,c,c,d} What about union R U S = ? Option 1 SUM R U S = {a,a,b,b,b,b,b,c,c,c,d} Option 2 MAX R U S = {a,a,b,b,b,c,c,d}

12. CS 4432logical query rewriting - lecture 1512 Which option makes this rule work ?  p1vp2 (R) =  p1 (R) U  p2 (R) Example: R={a,a,b,b,b,c} P1 satisfied by a,b; P2 satisfied by b,c  p1vp2 (R) = {a,a,b,b,b,c}  p1 (R) = {a,a,b,b,b}  p2 (R) = {b,b,b,c}  p1 (R) U  p2 (R) = {a,a,b,b,b,c} Let us try MAX():

13. CS 4432logical query rewriting - lecture 1513 Which option makes this rule work ?  p1vp2 (R) =  p1 (R) U  p2 (R) Example: R={a,a,b,b,b,c} P1 satisfied by a,b; P2 satisfied by b,c  p1vp2 (R) = {a,a,b,b,b,c}  p1 (R) = {a,a,b,b,b}  p2 (R) = {b,b,b,c}  p1 (R) U  p2 (R) = {a,a,b,b,b,b,b,b,c} What about Sum()?

14. CS 4432logical query rewriting - lecture 1514 Which option makes this rule work ?  p1  p2 (R)=  p1 [  p2 (R)] Example: R={a,a,b,b,b,c} P1 satisfied by a,b; P2 satisfied by b,c MAX or SUM ?

15. CS 4432logical query rewriting - lecture 1515 Option 2 (MAX) makes this rule work:  p1vp2 (R) =  p1 (R) U  p2 (R) Example: R={a,a,b,b,b,c} P1 satisfied by a,b; P2 satisfied by b,c  p1vp2 (R) = {a,a,b,b,b,c}  p1 (R) = {a,a,b,b,b}  p2 (R) = {b,b,b,c}  p1 (R) U  p2 (R) = {a,a,b,b,b,c}

16. CS 4432logical query rewriting - lecture 1516 Yet another example ! Senators (……)Reps (……) T1 =  yr,state Senators; T2 =  yr,state Reps T1 Yr State T2 Yr State 97 CA 99 CA 99 CA 99 CA 98 AZ 98 CA Union? “Sum” option makes more sense!

17. CS 4432logical query rewriting - lecture 1517 Decision -> In summary, we tend to use “SUM” option for bag union -> Thus great care must be taken, as some rules cannot be used for bags !

18. CS 4432logical query rewriting - lecture 1518 Rules: Project Let: X = set of attributes Y = set of attributes XY = X U Y  xy (R) =  x [  y (R)]

19. CS 4432logical query rewriting - lecture 1519 Let p = predicate with only R attributes q = predicate with only S attributes m = predicate with both R and S attribs  p (R S) =  q (R S) = Rules:  combined [  p (R)] S R [  q (S)]

20. CS 4432logical query rewriting - lecture 1520  p  q (R S) = ? Rules:  combined Rule can be derived !

21. CS 4432logical query rewriting - lecture 1521 Derivation for rule :  p  q (R S) =  p [  q (R S) ] =  p [ R  q (S) ] = [  p (R)] [  q (S)]

22. CS 4432logical query rewriting - lecture 1522 More Rules can be Derived:  p  q (R S) =  p  q  m (R S) =  pvq (R S) = Rules:  combined (continued)

23. CS 4432logical query rewriting - lecture 1523 We did one, do others on your own :  p  q (R S) = [  p (R)] [  q (S)]  p  q  m (R S) =  m [ (  p R) (  q S) ]  pvq (R S) = [ (  p R) S ] U [ R (  q S) ]

24. CS 4432logical query rewriting - lecture 1524 Rules:  combined Let x = subset of R attributes z = attributes in predicate P (subset of R attributes)  x [  p ( R ) ] =  {  p [  x ( R ) ] } x x  xz

25. CS 4432logical query rewriting - lecture 1525 Rules:  combined Let x = subset of R attributes y = subset of S attributes z = intersection of R,S attributes  xy (R S) =  xy { [  xz ( R ) ] [  yz ( S ) ] }

26. CS 4432logical query rewriting - lecture 1526 In textbook: more transformations More rewrite rules Other operations, such as, duplicate elimination, etc. Eliminate common sub-expressions Identify contradictions

27. CS 4432logical query rewriting - lecture 1527  xy {  p (R S) } =  xy {  p [  xz’ (R)  yz’ (S)] } z’ = z U { attributes used in P }

28. CS 4432logical query rewriting - lecture 1528 Rules for    combined with X similar... e.g.,  p (R X S) = ?

29. CS 4432logical query rewriting - lecture 1529  p (R U S) =  p (R) U  p (S)  p (R - S) =  p (R) - S =  p (R) -  p (S) Rules   U  combined:

30. CS 4432logical query rewriting - lecture 1530 Which are “good” transformations?

31. CS 4432logical query rewriting - lecture 1531 Conventional wisdom: do projects early Example: relation R(A,B,C,D,E) predicate P: (A=3)  (B=“cat”)  E {  p (R)} vs.  E {  p {  ABE (R)} }

32. CS 4432logical query rewriting - lecture 1532 What if we have A, B indexes? B = “cat” A=3 Intersect pointers to get pointers to matching tuples! But Then better to do projection later !

33. CS 4432logical query rewriting - lecture 1533  p1  p2 (R)   p1 [  p2 (R)]  p (R S)  [  p (R)] S R S  S R  x [  p (R)]   x {  p [  xz (R)] } Which are “good” transformations?

34. CS 4432logical query rewriting - lecture 1534 Bottom line: Some heuristics : –Early selection is usually good No transformation is always good Rule application defines a search space –Need cost criteria to make decision