Distributed Database Management Systems: Lecture 15

Distributed Database
Management Systems

Lecture 15


PHF- Minimality of Pr

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• A relevant predicate is the one if it
influences how fragmentation is
performed (fragments f into fi and fj)
then there should be at least one
application that accesses fi and fj
differently.
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If all predicates in a set Pr are
relevant then the set is minimal

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PHF-COM-MIN Algorithm

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• Given: a relation R and a set of
simple predicates Pr.
• Output: a complete and minimal set of
simple predicates Pr’ for Pr.

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• Rule 1: a relation or fragment is
partitioned into at least two parts
which are accessed differently by at
least one application.

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1-Initialization:
–Find a pi ∈ Pr such that pi,

partitions R according to Rule 1
Pr’ ← pi
Pr ← Pr – pi

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2- Iteratively add predicates to Pr' until it is
complete, find a pj ∈ Pr such that pj
partitions R according to Rule 1
set Pr' = Pr' U pi ;
Pr = Pr – pi ;

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if pk in Pr' is non-relevant then
Pr' = Pr' – pk

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Primary Horizontal Partitioning
Algorithm

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• Makes use of COM_MIN to perform
fragmentation
• Input: a relation R and a set of simple
predicates Pr

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• Output: a set of minterm
predicates M according to which
relation R is to be fragmented

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• Pr‘ ← COM_MIN (R,Pr)
• determine the set M of minterm
predicates

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• determine the set I of implications
among pi Pr
• eliminate the contradictory
minterms from M

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PHF – Example II

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1 Find the name and budget of projects
given their no. issued at three sites
– p1 : LOC = "Lahore”
– p2 : LOC = “Rawalpindi"
– p3 : LOC = "Peshawar“

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2 Access project information according to
budge one site accesses ≤ 200000 other
accesses >200000
– p4 : BUDGET ≤ 200000
– p5 : BUDGET > 200000

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Pr = Pr' = {p1 ,p2 ,p3 ,p4 ,p5 }
• Implications
p2 p3
• p1
• p4

p5

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• From predicates p1 to p6 in Pr’, there
may be so many minterm predicates,
like,
p1 ^ p2 ^ p3 ^ p4 ^ p5

Excluding the contradicting minterm
predicates

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–m1 : (LOC = "Lahore") ^ (BUDGET ≤ 2M)
–m2 : (LOC = "Lahore") ^ (BUDGET > 2M)
–m3 : (LOC = " Rawalpindi ") ^ (BUDGET ≤ 2M)
–m4 : (LOC = "Rawalpindi") ^ (BUDGET > 2M)
–m5 : (LOC = "Peshawar") ^ (BUDGET ≤ 2M)
–m6 : (LOC = "Peshawar") ^ (BUDGET > 2M)

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• Implications must be based on the
database semantics not on a
particular extension of the
database

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PROJ
pNo

pName

budget

Loc

P1

Instrumentation

3.5M

Lahore

P2

Database Dev.

2.3M

Rawalpindi

P3

CAD/CAM

1.9M

Rawalpindi

P4

Maintenance

1.6M

Peshawar

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pNo

pName

budget

Loc

P1

Instrumentation

3.5M

Lahore

P2

Database Dev.

2.3M

Rawalpindi

P3

CAD/CAM

1.9M

Rawalpindi

P4

Maintenance

1.6M

Peshawar

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Derived Horizontal
Fragmentation(DHF)

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