1. Distributed Database Management Systems Lecture 15

2. Virtual University of Pakistan 2 PHF- Minimality of Pr

3. Virtual University of Pakistan 3 A relevant predicate is the one if it influences how fragmentation is performed (fragments f into f i and f j )A relevant predicate is the one if it influences how fragmentation is performed (fragments f into f i and f j ) then there should be at least one application that accesses f i and f j differently. then there should be at least one application that accesses f i and f j differently.

4. Virtual University of Pakistan 4 If all predicates in a set Pr are relevant then the set is minimal If all predicates in a set Pr are relevant then the set is minimal

5. Virtual University of Pakistan 5 PHF-COM-MIN Algorithm

6. Virtual University of Pakistan 6 Given: a relation R and a set of simple predicates P r.Given: a relation R and a set of simple predicates P r. Output: a complete and minimal set of simple predicates P r ’ for P r.Output: a complete and minimal set of simple predicates P r ’ for P r.

7. Virtual University of Pakistan 7 Rule 1: a relation or fragment is partitioned into at least two parts which are accessed differently by at least one application.Rule 1: a relation or fragment is partitioned into at least two parts which are accessed differently by at least one application.

8. Virtual University of Pakistan 8 1-Initialization: –Find a p i ∈ Pr such that p i, partitions R according to Rule 1 Pr’ ← p i Pr’ ← p i Pr ← Pr – p i Pr ← Pr – p i

9. Virtual University of Pakistan 9 2- Iteratively add predicates to Pr' until it is complete, find a p j ∈ Pr such that p j partitions R according to Rule 1 set Pr' = Pr' U p i ; set Pr' = Pr' U p i ; Pr = Pr – p i ; Pr = Pr – p i ;

10. Virtual University of Pakistan 10 if p k in Pr' is non-relevant then Pr' = Pr' – p k

11. Virtual University of Pakistan 11 Primary Horizontal Partitioning Algorithm

12. Virtual University of Pakistan 12 Makes use of COM_MIN to perform fragmentation Input: a relation R and a set of simple predicates Pr

13. Virtual University of Pakistan 13 Output: a set of minterm predicates M according to which relation R is to be fragmented

14. Virtual University of Pakistan 14 Pr‘ ← COM_MIN (R,Pr) determine the set M of minterm predicates

15. Virtual University of Pakistan 15 determine the set I of implications among pi  Pr eliminate the contradictory minterms from M

16. Virtual University of Pakistan 16 PHF – Example II

17. Virtual University of Pakistan 17 1 Find the name and budget of projects given their no. issued at three sites –p1 : LOC = "Lahore” –p2 : LOC = “Rawalpindi" –p3 : LOC = "Peshawar“

18. Virtual University of Pakistan 18 2 Access project information according to budge one site accesses ≤ 200000 other accesses >200000 –p4 : BUDGET ≤ 200000 –p5 : BUDGET > 200000

19. Virtual University of Pakistan 19 Pr = Pr' = {p1,p2,p3,p4,p5 } ImplicationsImplications p 1   p 2   p 3p 1   p 2   p 3 p 4   p 5p 4   p 5

20. Virtual University of Pakistan 20 From predicates p1 to p6 in Pr’, there may be so many minterm predicates, like,From predicates p1 to p6 in Pr’, there may be so many minterm predicates, like, p1 ^ p2 ^ p3 ^ p4 ^ p5 Excluding the contradicting minterm predicates

21. Virtual University of Pakistan 21 –m1 : (LOC = "Lahore") ^ (BUDGET ≤ 2M) –m2 : (LOC = "Lahore") ^ (BUDGET > 2M) –m3 : (LOC = " Rawalpindi ") ^ (BUDGET ≤ 2M) –m4 : (LOC = "Rawalpindi") ^ (BUDGET > 2M) –m5 : (LOC = "Peshawar") ^ (BUDGET ≤ 2M) –m6 : (LOC = "Peshawar") ^ (BUDGET > 2M)

22. Virtual University of Pakistan 22 Implications must be based on the database semantics not on a particular extension of the databaseImplications must be based on the database semantics not on a particular extension of the database

23. Virtual University of Pakistan 23 pNopNamebudgetLoc P1Instrumentation3.5MLahore P2 Database Dev. 2.3MRawalpindi P3CAD/CAM1.9MRawalpindi P4Maintenance1.6MPeshawar PROJ

24. Virtual University of Pakistan 24 pNopNamebudgetLoc P1Instrumentation3.5MLahore P2 Database Dev. 2.3MRawalpindi P3CAD/CAM1.9MRawalpindi P4Maintenance1.6MPeshawar

25. Virtual University of Pakistan 25 Derived Horizontal Fragmentation(DHF)

26. Virtual University of Pakistan 26 Defined on a member relation of a link according to a selection operation specified on its ownerDefined on a member relation of a link according to a selection operation specified on its owner

27. Virtual University of Pakistan 27 Two important points:Two important points: –Each link is an equi-join. –Equijoin can be implemented by means of semi-joins

28. Virtual University of Pakistan 28 So we are interested in defining the partitions of member based on fragmentation of its owner, but want to see attributes only from member, soSo we are interested in defining the partitions of member based on fragmentation of its owner, but want to see attributes only from member, so

29. Virtual University of Pakistan 29 R i = R ⋉ S i, 1≤ i ≤ w where w is the maximum number of fragments that will be defined on R and where w is the maximum number of fragments that will be defined on R and Si =  Fi (S), where Fi is formula for PHF on S Si =  Fi (S), where Fi is formula for PHF on S

30. Virtual University of Pakistan 30 DHF Example

31. Virtual University of Pakistan 31 title, sal eNo, Name, titkejNo, jName, budget, loc eNo, jNo, resp, dur PAY EMP ASIGN PROJ L1

32. Virtual University of Pakistan 32 Considering the link L1 above: owner (L1) = PAY member (L1) = EMP We want to group employees on the basis of their salaries one with salary less than or equal to 30,000/- and other more than that

33. Virtual University of Pakistan 33 eNoeNametitle E1 T Khan Elec Eng E2 W Shah Sys Ana E3 R Dar Mech Eng E4 K Butt Programme E5 F Sahbai Sys Ana E6 A Haq Elec Eng E7 S Farhana Mech Eng E8 M Daud Sys Ana

34. Virtual University of Pakistan 34 TitleSal Elect. Eng 40000 Sys Analyst 34000 Mech. Eng 27000 Programmer24000

35. Virtual University of Pakistan 35 E3 R Dar Mech Eng E4 K Butt Programme E7 S Farhana Mech Eng eNoeNametitleE1 T Khan Elec Eng E2 W Shah Sys Ana E5 F Sahbai Sys Ana E6 A Haq Elec Eng E8 M Daud Sys Ana

36. ThanksThanks