1. Distributed Database Management Systems
Lecture 17

2. Virtual University of Pakistan
In this Lecture
Continue with VF
Information Requirement
Attribute affinities
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Replication of Key attributes does not violate the disjoint ness condition
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4. Vertical Fragmentation Information Requirements
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Basic idea of VF is access efficiency
Information Requirement is application based
Attribute affinities: obtained from more primitive usage data
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(80-20 Rule)
Attribute usage values: Given a set of queries Q = {q1 , q2 ,…, qq} that will run on the relation R[A1, A2 ,…, An]
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Attribute Usage Value
use(qi,Aj )
1 if attribute Aj is
referenced by query qi
use(qi,Aj ) =
0 otherwise
use(qi,• ) can be defined accordingly
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8. Virtual University of Pakistan
PROJ(jNo, jName, budget, loc)
q1: SELECT BUDGET FROM PROJ WHERE
JNO=Value
q2: SELEC JNAME, BUDGET FROM PROJ
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q3: SELECT JNAME FROM PROJ
WHERELOC=Value
q4: SELECTSUM(BUDGET) FROM PROJ
WHERE LOC=Value
Let A1= jNo, A2= jName, A3= budget, A4= loc
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A1 A2 A3 A4 q1 q2 q3 q4
Attribute Usage Matrix
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AUM does not represent the query frequency at different sites;
Attribute affinity between two attribute Ai and Aj, affinity (Ai, Aj), of a relation R(A1, A2, …., An) with respect to applications set
Q = {q1, q2, …, qq) is
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aff(Ai, Aj) =
∑ ∑ refl(qk)accl(qk)
k|use(qk, Ai) = 1  use(qk, Aj) = 1∀ sites
where refl(qk) is number of accesses to attributes (Ai, Aj) for each execution of qk at site Sl, and…
accl(qk) is application access frequency measure from Sl
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Attribute Usage
Matrix S1 S2 S3 q1 15 20 10 q2 5 q3 25 q4 3 A1 A2 A3 A4 q1 1 q2 q3 q4
Access Frequency
Matrix
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acc1(q1) = 15, acc2(q1) = 20, acc3(q1) = 10
acc1(q2) = 5, acc2(q2) = 0, acc3(q2) = 0
acc1(q3) = 25, acc2(q3) = 25, acc3(q3) = 25
acc1(q4) = 3, acc2(q4) = 0, acc3(q4) = 0
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aff(A3, A4)
= ∑k = 4 ∑l =1..3 refl(qk)accl(qk)
= 3 * = 3
aff(A1, A2) = 0,
Since no qi accesses them both
aff(A2, A2) = 5 * = 5
25 * * * 1 = = 80
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16. Virtual University of Pakistanq1 15 20 10 q2 5 q3 25 q4 3 A1 A2 A3 A4 q1 1 q2 q3 q4
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Attribute affinity matrix (AA) A1 A2 A3 A4 45 80 5 75 53 3 78
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18. Clustering Algorithm

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VF is based on identifying groups of attributes based on AA
Vertical Clustering is based on Bond Energy Algorithm (BEA); it uses AA; identifies groups of similar items
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Large affinity attributes are combined together and lower together
BEA takes as input the AA and generates the cluster affinity matrix CA
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21. Global Affinity Measure (AM)

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Affinity Measure is a single value that is calculated on the basis of positions of elements in AA and their surrounding elements
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23. Virtual University of Pakistan45 80 5 75 53 3 78
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AM = ∑ n
i = 1
j = 1 ∑
aff(Ai, Aj) [aff(Ai, Aj-1) + aff(Ai, Aj+1)
+ aff(Ai-1, Aj) + aff(Ai+1, Aj) ]
aff(A0, Aj)= aff(Ai, A0)=
aff(An+1, Aj)= aff(Ai, An+1)=0
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25. Virtual University of Pakistan45 80 5 75 53 3 78
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