## Description

1. Consider the relation PAY in Figure below. Suppose there is one application

that access PAY. It is using ‘TITLE’ in PAY included in its simple predicates.

1) Find all possible simple predicates for ‘TITLE’ in PAY.

2) Derive the primary horizontal fragmentation of PAY using the simple

predicates in 1).

3) Using the fragmentation of PAY in 2), perform a derived horizontal

fragmentation for EMP.

4) Using the fragmentation of EMP in 3), perform a derived horizontal

fragmentation for ASG.

2. Consider relations ASGand PROJin Figure above. ASGand PROJare

horizontally fragmented asfollows:

ASG1 = σ PNO = “P1”(ASG)

ASG2 = σ PNO = “P2”( ASG)

ASG3 =σ PNO = “P3”( ASG)

ASG4 =σ PNO = “P4”( ASG)

PROJ1 =σ BUDGET ≥ 200000 (PROJ)

PROJ2 =σ BUDGET < 200000 (PROJ)

1) Draw the join graph of ASG ⋉PNO PROJ. Isthe graph simple or partitioned?

2) If it is partitioned, modify the fragmentation of ASG so that the join graph of

ASG ⋉PNO PROJ issimple, and provide new fragmentation.

3) Draw the join graph(s) based on the new fragmentation.

3. Let Q = {q1, q2, q3, q4, q5} be a set of queries, A = {A1, A2, A3, A4, A5} be a set

of attributes, and S = {S1, S2, S3} be a set of sites. The matrix of Figure (a)

below describes the attribute usage values, and the matrix of Figure (b) gives

the application access frequencies. Assume that refs (qk ) = 1 for all qk and Si .

1) Derive an AA (Attribute Affinity) matrix (Provide all the details how to get it).

2) Derive a CA (Clustered Affinity) matrix using the bond energy algorithm

(Provide all the details how to get it).

3) Using the partitioning algorithm (Z = CTQ∗CBQ−COQ2

), partition the

attributes in the above CA to two partitions.

A1 A2 A3 A4 A5 S1 S2 S3

Q1 1 0 0 1 0 Q1 20 30 0

Q2 1 1 1 0 0 Q2 10 0 15

Q3 0 0 0 1 1 Q3 0 45 15

Q4 1 0 1 0 0 Q4 0 20 0

Q5 0 1 0 1 1 Q5 0 25 0

(a) (b)