Distributed Database Management Systems: Lecture 17

Distributed Database
Management Systems

Lecture 17


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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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 )
use(qi,Aj ) =

1 if attribute Aj is 
    referenced by query qi
0 otherwise

use(qi,• ) can be defined accordingly
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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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q1
q2
q3
q4

A1  

A2

A3

A4

1
0
0
0

0
1
1
0

1       0
1   
0
0       1
1            1

Attribute Usage Matrix
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• AUM does not represent the query frequency at
different sites;
• Attribute affinity between two attribute A i 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) =

∑
k|use(qk, Ai) = 1

∑ refl(qk)accl(qk)
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
A
A
A
A

S1

S2

S3

1

2

3

4

q1

1

0

1

0

q1

15

20

10

q2

0

1

1

0

q2

5

0

0

q3

0

1

0

1

q3

25

25

25

q4

0

0

1

1

q4

3

0

0

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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 *1 + 0 + 0 = 3
aff(A1, A2) = 0, 
Since no qi accesses them both
aff(A2, A2) =  5 * 1 + 0  + 0  = 5
25 * 1 + 25 *1 + 25 * 1 = 75 + 5 = 80
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S1

S2

S3

q1

15

20

10

0

q2

5

0

0

0

1

q3

25

25

25

1

1

q4

3

0

0

A1

A2

A3

A4

q1

1

0

1

0

q2

0

1

1

q3

0

1

q4

0

0

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Attribute affinity matrix (AA) 
A1

A2

A3

A4

A1

45

0

45

0

A2

0

80

5

75

A3

45

5

53

3

A4

0

75

3

78

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Clustering Algorithm


• 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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Global Affinity
Measure (AM)


• 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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A1

A2

A3

A4

A1

45

0

45

0

A2

0

80

5

75

A3

45

5

53

3

A4

0

75

3

78

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n

n

∑ ∑ aff(Ai, Aj) [aff(Ai, Aj­1) + aff(Ai, Aj+1) 
              + aff(Ai­1, Aj) + aff(Ai+1, Aj) ]

AM = 
i = 1 j = 1

aff(A0, Aj)= aff(Ai, A0)=
aff(An+1, Aj)= aff(Ai, An+1)=0

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A1

A2

A3

A4

A1

45

0

45

0

A2

0

80

5

75

A3

45

5

53

3

A4

0

75

3

78

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