1. CS 44321 CS4432: Database Systems II Logical Plan Rewriting

2. CS 4432query processing2 parse convert apply laws estimate result sizes consider physical plans estimate costs pick best execute {P1,P2,…..} {(P1,C1),(P2,C2)...} Pi answer SQL query parse tree logical query plan “improved” l.q.p l.q.p. +sizes statistics

3. CS 44323 Query in SQL  Query Plan in Algebra (logical)  Other Query Plan in Algebra (logical)

4. CS 44324 Query plan 1 (in relational algebra)  B,D  R.A =“c”  S.E=2  R.C=S.C  X RS

5. CS 44325 Query plan 2 (in relational algebra)  B,D  R.A = “c”  S.E = 2 R S natural join on R.C=S.C

6. CS 44326 Relational algebra optimization What are transformation rules ? –preserve equivalence What are good transformations? –reduce query execution costs

7. CS 44327 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.:

8. CS 44328 Rules: Other binary operators ? R S=SR (R S) T= R (S T) What about : Cross product? Condition join? Union? Intersection ? Difference ?

9. CS 44329 Note: T R R SS T

10. CS 443210 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)

11. CS 443211 Rules: Selects  p1  p2 (R)=  p1 [  p2 (R)] [  p1 (R)] U [  p2 (R)]  p1vp2 (R) =

12. CS 443212 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}

13. CS 443213 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():

14. CS 443214 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()?

15. CS 443215 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 What about MAX versus SUM ?

16. CS 443216 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}

17. CS 443217 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!

18. CS 443218 Executive Decision -> Use “SUM” option for bag unions -> CAREFUL ! Some rules cannot be used for bags

19. CS 443219 Rules: Project Let: X = set of attributes Y = set of attributes XY = X U Y  xy (R) =  x [  y (R)]

20. CS 443220 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)]

21. CS 443221  p  q (R S) = ? Rules:  combined Rule can be derived !

22. CS 443222 Derivation for rule :  p  q (R S) =  p [  q (R S) ] =  p [ R  q (S) ] = [  p (R)] [  q (S)]

23. CS 443223 More Rules can be Derived:  p  q (R S) =  p  q  m (R S) =  pvq (R S) = Rules:  combined (continued)

24. CS 443224 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) ]

25. CS 443225 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

26. CS 443226 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 ) ] }

27. CS 443227  xy {  p (R S) } =  xy {  p [  xz’ (R)  yz’ (S)] } z’ = z U { attributes used in P }

28. CS 443228  p (R U S) =  p (R) U  p (S)  p (R - S) =  p (R) - S =  p (R) -  p (S) Rules   U  combined:

29. CS 443229 Which are “good” transformations?

30. CS 443230 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)} }

31. CS 443231 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 !

32. CS 443232  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?

33. CS 443233 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

34. CS 443234 In textbook: more transformations Chapter 16.2, 16.3.3 More rewrite rules Other operations, such as, duplicate elimination, etc.