1. Distributed Database Management Systems
Lecture 20

2. In the Previous Lecture
Continued with VF
Computed CA
Partitioning Algorithm

3. In this Lecture Continue with VF Hybrid Fragmentation
Allocation Problem
Replication

4. A1 A3 A2 A4 45 53 5 3 80 75 78 A1 A2 A3 A4 q1 1 q2 q3 q4 S1 S2 S3 q1 15 20 10 q2 5 q3 25 q4 3 CA
refj(qi)
accj(qi)
z2 = 3311
z1 = 0 – 452
z3=

5. A1= jNo A2= jName
A3= budget A4= loc
V1 = {jNo, budget}
V2 = {jNo, jName, loc}

6. VF- Two Problems
1- Clusters not in the sides, rather in the middle of CA
2- m-way partitioning

7. VF Correctness

8. A relation R, defined over attribute set A and key K, generates the vertical partitioning
FR = {R1, R2 , …, Rr }
Completeness: The following should be true for A A =U Ri

9. Reconstruction: can be achieved by
R = ⋈K Ri, ∀Ri ∈ FR
Disjointness: TID's are not considered to be overlapping since they are maintained by the system
PK is exception

10. Hybrid Fragmentation

11. Practically, applications require the fragmentation of both the types to be combined

12. So the nesting of fragmentations, i. e
So the nesting of fragmentations, i.e., one following the other, it becomes sort of a tree

13. Disjoint ness and completeness have to be assured at each step, and reconstruction can be obtained by applying Join and Union in reverse order

14. CUST Beta Delta1 Delta2 A/C# Name Bal Branch AB101 Saeed 4535 MTN
Laeeq
LHR
AB203
Salma
AB109
Shaan
45.32
CUST
Beta = ΠA/C#, Bal (CUST)
Delta1 = σ Loc = “MTN” (ΠA/C#, Name, Branch (CUST))
Delta2 = σ Loc = “LHR” (ΠA/C#, Name, Branch (CUST))
Beta
A/C#
Bal
AB101
4535
AB202
AB203
AB109
45.32
Delta1
Delta2
A/C#
Name
Branch
AB101
Saeed
MTN
AB109
Shaan
A/C#
Name
Branch
AB202
Laeeq
LHR
AB203
Salma

15. Allocation

16. Find the "optimal" distribution of F to S.
Given F = {F1, F2 , …, Fn} fragments
S ={S1 , S2 , …, Sm} network sites
Q = {q1, q2 ,…, qq } applications
Find the "optimal" distribution of F to S.

17. Optimality
Minimize the processing cost and maximize the system throughput at each site

18. It is a complex problem to be solved mathematically, to make the things very simple, consider the allocation of a single fragment Fk,

19. set of read only queries on Fk from Si; T = {t1, t2, …, tm}
set of update queries U on Fk from Si;
U= {u1, u2, .., um}

20. Communication Cost
C(T) = {c1,2, c1,3, …., c1,m, ….cm-1, m}
C’(T) = {c’1,2, c’1,3, …., c’1,m, ….c’m-1, m}
Storage Cost
D = {d1, d2, ……., dm}

21. Allocation problem is to find the cites out of set of sites S, where the copy of Fk will be stored.

22. The specification of the allocation problem will be
0 otherwise
xj =
1 if the fragment Fk is assigned to site Sj
The specification of the allocation problem will be
min

23. That concludes our discussion on Fragmentation
Lets summarize it

24. Fragmentation is splitting a table into smaller tables Alternatives
Horizontal
Vertical
Hybrid

25. Horizontal Fragmentation

26. Splits a table into horizontal subsets (row wise)
Primary and Derived Horizontal Fragmentation

27. We need major simple predicates (Pr); should be complete & minimal
Pr is transformed into Pr’
Minterm (M) predicates from Pr’

28. Correctness of PHF depends on the Pr’
Derived Horizontal Fragmentation is based on Owner-member link

29. Vertical Fragmentation is more complicated due to more options
Based on attributes’ affinities

30. AA is transformed into CA using BEA
Calculated using usage data and access frequencies from different sites
AA is transformed into CA using BEA

31. CA establishes clusters of attributes that are split for efficient access
Hybrid Fragmentation combines HF and VF
That concludes Fragmentation

32. Thanks