1. Distributed Database Management Systems
Lecture 32

2. In the previous lecture
Query Processing
Query Decomposition
Its Different Phases.

3. In this Lecture Final phase of QD
Next phase of Query Optimization: Data Localization.

4. A1, ….,An(p(Ap)(R))  ((p(Ap) A1, ….,An, Ap(R)))-
3- Idempotency of unary Ops
i) A’(A”(R))  A’(R)
ii) σp1(A1)(σp2(A2)(R)) 
σp1(A1) ∧ p2(A2)(R)-
4- Commuting selection with projection
A1, ….,An(p(Ap)(R))  ((p(Ap) A1, ….,An, Ap(R)))-

5. 5- Commuting Selection with binary ops, like join and CP
6- Commuting Projection with binary ops, like join and CP

6. Many equivalence query trees can be generated
Comparing all such trees to select best is not feasible
Heuristic is applied

7. Separation of Unary Ops
Unary ops on the same relation grouped together
Unary ops commuted with binary ops
Binary ops are ordered

8. ASN
PROJ
EMP x
⋈ pNo^eNo
 (pName = ‘CAD/CAM’)^ (dur = 12 v dur = 24)^ eName ’Saleem’
 eName

9. PROJ ASG EMP  pNo’  pNo, eNo  eNo, eName  pNo, eName  eName
pName = ‘CAD/CAM’
dur=12 v dur = 24
eName != ‘Saleem’
 pNo’
 pNo, eNo
 eNo, eName
 pNo, eName
 eName

10. This concludes Query Decomposition and Restructuring
Concerns both centralized and distributed environments

11. Now we move to the second phase of Query Optimization; Data Localization of DD
QD at global level, this phase transform into local ones (fragments)

12. Called Localization Program
A Naïve rule…
However, it won’t be an efficient one

13. Reduction During Data Localization

14. Example Schema EMP(eNo, eName, title) Horizontal Fragmentation
EMP1 = eNo ≤ ‘E3’ (EMP)
EMP2 = ’E3’<eNo ≤ ‘E6’ (EMP)
EMP3 = eNo > ‘E6’ (EMP)

15. Reduction with Selection Rule 1:
pi (Rj) = Ø if ∀x in Rj: (pi(x) ^ pj(x))
That is, there exist conflicting predicates

16. Select * from EMP where eNo = ‘E7’U
eNo = ‘E7’
EMP3
eNo = ‘E7’
Smart thinking
Naïve Rule

17. Reduction on Join
Distributing joins over unions and avoiding unnecessary joins
(R1UR2) ⋈ R3= (R1 ⋈ R3) U (R2 ⋈ R3)

18. Rule2:
Ri⋈Rj = Ø if ∀x in Ri and ∀y in Rj:(pi(x) ^ pj(x))
Useless joins can be determined viewing the join predicates

19. Remember! Reduced query is not always better. We have to be watchful-
Parallel Execution
ASG1 = eNo ≤ ‘E3’ (ASG)
ASG2 = ’eNo > ‘E3’ (ASG).

20. Select eName
From EMP, ASG
Where EMP.eNo = ASG. eNo.

21. We already know about PHF of EMP
⋈eNo
ASG1
ASG2
Generic Query

22. EMP1 U
⋈eNo
ASG1
EMP2
ASG2
EMP3
Reduction for PHF with JOIN

23. Reduction for VF
Relation fragmented on projection, with PK as the common attribute
Localization involves natural join on PK

24. EMP1 = eNo, eName (EMP)
EMP2 = eNo, title (EMP)
Relation R defined over attributes A = {A1, ..., An} vertically fragmented as Ri = A' (R) where A'  A

25. Rule3: D,K(Ri) is useless if the set of projection attributes D is not in A‘.

26. Example: Select eName from EMP ⋈eNo Generic Query Reduced Query

27. Reduction for DF Relation R is fragmented based on the predicate on S
DF should be done for hierarchical relationship between R and S-

28. Example
ASG1: ASG ⋉ ENO EMP1
ASG2: ASG ⋉ ENO EMP2
EMP1: σ title= ‘Programmer’ (EMP)
EMP2: σ title “Programmer’ (EMP).

29. Query
SELECT * FROM EMP, ASG WHERE ASG.eNo = EMP.eNo AND EMP.title = "Mech. Eng."

30. ASG1
⋈eNo U
ASG2
EMP1
EMP2
title = ‘Mech Eng.’
Generic Query

31. Pushing Selection Down
ASG1
⋈eNo U
ASG2
EMP2
title = ‘Mech Eng.’
Pushing Selection Down
⋈eNo

32. ASG1
⋈eNo U
EMP2
ASG2
title = ‘Mech Eng.’
Union Moved Up

33. ⋈eNo
ASG2
EMP2
title = ‘Mech Eng.’
Optimal Reduced Query

34. Thanks