Distributed DatabaseManagement Systems

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Derived Horizontal Fragmentation(DHF)

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• Defined on a member relation of a link according to a selection operation specified on its owner

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• Two important points:– Each link is an equi-join.– Equijoin can be implemented by means of

semi-joins

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• So we are interested in defining the partitions of member based on fragmentation of its owner, but want to see attributes only from member, so

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Ri = R S⋉ i, 1≤ i ≤ w 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

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DHF Example

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title, sal

eNo, Name, titke jNo, jName, budget, loc

eNo, jNo, resp, dur

PAY

EMP

ASIGN

PROJ

L1

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• 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

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eNo eName title

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

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Title Sal

Elect. Eng 40000

Sys Analyst 34000

Mech. Eng 27000

Programmer 24000

E3 R Dar Mech Eng

E4 K Butt Programme

E7 S Farhana Mech Eng

eNo eName title

E1 T Khan Elec Eng

E2 W Shah Sys Ana

E5 F Sahbai Sys Ana

E6 A Haq Elec Eng

E8 M Daud Sys Ana

• PAY1 = σ sal ≤ 30000 (PAY)

• PAY2 = σ sal > 30000 (PAY)

• EMP1 = EMP PAY1⋉• EMP2 = EMP PAY2⋉

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DHF• The inputs required for DHF

– The set of partitions for owner– Member relation– Semi-join predicates between owner and

member

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DHA• Care in case of multiple owners, like

ASIGN• Fragmentation selection depends:

1- One with better Join Characteristics2- One used in more applications

• Second one is straight forward, we should try to facilitate heavy users; the first one needs more considerations

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DHF • For the first point;

– Join is performed on smaller relations, that increases efficiency

– The join can be performed in parallel in case of simple graphs, that improves efficiency as well; simple graph means

PAY1

EMP1

PAY2

EMP2

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DHF• demonstrates two things 1-Derived fragmentation may follow a chain, like

PAY-EMP-ASIGN 2-Typically, more than one fragmentation options are

there, which one adopted is an allocation problem discussed later

Checking for Correctness Completeness: for PHF depends on Pr’, and in DHF,

completeness of owner Pr’, and the referential integrity constraint

Reconstruction: Involves Union in both casesDisjointness: Simple in PHF if the pi in Pr’ are mutually

exclusive; in DHF, guaranteed in case of simple join graph, however in case of partitioned join graph it is hard to establish

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Checking for Correctness

Completeness: for PHF depends on Pr’, and in DHF, completeness of owner Pr’, and the referential integrity constraintLet R be member S be owner

Fs = { S1,S2,…Sn}‘A’ the common attribute

t[A] = t’ [A]

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Reconstruction:

Involves Union in both cases

FR = {R1,R2,….Rn} R = U Ri Ri FR∀ ∈

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Disjoint ness:

Simple in PHF if the pi in Pr’ are mutually exclusive; in DHF, guaranteed in case of simple join graph, however in case of partitioned join graph it is hard to establish

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Vertical Fragmentation (VF)• Vertical subset of relation • A VF of a relation produces fragments

R1, R2, …. Rn, each of which contains subset of attributes of R and PK of R.

• Objective is to produce smaller relations, so that most of the applications run on smaller relations; so they become fast.

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Vertical Fragment

• Vertical fragmentation is more complicated, since more alternatives exist.

• VF is mainly based on heuristics

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Example of VF

A/C# Name

Bal Branch

AB101

Saeed

4535 MTN

AB202

Laeeq

45632.34

LHR

AB203

Salma

67839.87

LHR

AB109

Shaan

45.32 MTNA/C# Na

meBranch

AB101

Saeed

MTN

AB202

Laeeq

LHR

AB203

Salma

LHR

AB109

Shaan

MTN

CUST

A/C# Bal

AB101

4535

AB202

45632.34

AB203

67839.87

AB109

45.32

Delta

Delta = ΠA/C#, Name, Branch (CUST)

Beta = ΠA/C#, Bal (CUST)

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Two Alternatives of VF

• Grouping: Starting with single attribute VFs and then combining different attributes

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Two Alternatives of VF

• Splitting: Starting from the whole relation and then breaking it down analyzing the nature of applications

• Later suits better to DDB environment; results non-overlapping fragments; so discussed here

Thanks