distributed database management systems lecture 15

Distributed Database Distributed Database Management Systems Management Systems Distributed Database Distributed Database

Management Systems Management Systems

Lecture 15Lecture 15

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PHF- Minimality of PrPHF- Minimality of PrPHF- Minimality of PrPHF- Minimality of Pr

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• A relevant predicate is the one if it A relevant predicate is the one if it influences how fragmentation is influences how fragmentation is performed (fragments f into fperformed (fragments f into fii and f and fjj))

then there should be at least one then there should be at least one application that accesses fapplication that accesses fii and f and fjj

differently. differently.

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If all predicates in a set Pr are If all predicates in a set Pr are relevant then the set is minimalrelevant then the set is minimal

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PHF-COM-MIN AlgorithmPHF-COM-MIN AlgorithmPHF-COM-MIN AlgorithmPHF-COM-MIN Algorithm

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• Given: a relation Given: a relation RR and a set of and a set of simple predicates simple predicates PPrr..

• Output: a complete and minimal set of Output: a complete and minimal set of simple predicates simple predicates PPrr’’ for for PPrr..

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

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1-Initialization:1-Initialization:–Find a pFind a pii Pr such that p∈ Pr such that p∈ ii, ,

partitions R according to Rule 1partitions R according to Rule 1

Pr’ ← pPr’ ← pii

Pr ← Pr – pPr ← Pr – pii

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2- Iteratively add predicates to 2- Iteratively add predicates to Pr' Pr' until it is until it is complete, find a complete, find a ppj j ∈ ∈ Pr Pr such that such that ppjj partitions R according to partitions R according to Rule 1Rule 1

set set Pr' Pr' = = Pr' U pPr' U pii ; ;

Pr = Pr Pr = Pr – – ppii ; ;

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if if ppkk in Pr' in Pr' is non-relevant thenis non-relevant then

Pr' = Pr' Pr' = Pr' – – ppkk

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Primary Horizontal Partitioning Algorithm

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 IIPHF – Example IIPHF – Example IIPHF – Example II

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

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

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Pr Pr = = Pr' Pr' = = {p{p1 1 ,p,p2 2 ,p,p3 3 ,p,p4 4 ,p,p5 }5 }

• ImplicationsImplications

• pp11 pp22 pp33

• pp44 pp55

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• From predicates p1 to p6 in Pr’, there From predicates p1 to p6 in Pr’, there may be so many minterm predicates, may be so many minterm predicates, like, like,

p1 ^ p2 ^ p3 ^ p4 ^ p5p1 ^ p2 ^ p3 ^ p4 ^ p5

Excluding the contradicting minterm Excluding the contradicting minterm predicatespredicates

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–m1 : (LOC = "Lahore") ^ (BUDGET ≤ 2M)m1 : (LOC = "Lahore") ^ (BUDGET ≤ 2M)

–m2 : (LOC = "Lahore") ^ (BUDGET > 2M)m2 : (LOC = "Lahore") ^ (BUDGET > 2M)

–m3 : (LOC = " Rawalpindi ") ^ (BUDGET ≤ 2M)m3 : (LOC = " Rawalpindi ") ^ (BUDGET ≤ 2M)

–m4 : (LOC = "Rawalpindi") ^ (BUDGET > 2M)m4 : (LOC = "Rawalpindi") ^ (BUDGET > 2M)

–m5 : (LOC = "Peshawar") ^ (BUDGET ≤ 2M)m5 : (LOC = "Peshawar") ^ (BUDGET ≤ 2M)

–m6 : (LOC = "Peshawar") ^ (BUDGET > 2M)m6 : (LOC = "Peshawar") ^ (BUDGET > 2M)

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

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pNopNo pNamepName budgetbudget LocLoc

P1P1 InstrumentationInstrumentation 3.5M3.5M LahoreLahore

P2P2 Database Dev.Database Dev. 2.3M2.3M RawalpindiRawalpindi

P3P3 CAD/CAMCAD/CAM 1.9M1.9M RawalpindiRawalpindi

P4P4 MaintenanceMaintenance 1.6M1.6M PeshawarPeshawar

PROJ

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pNopNo pNamepName budgetbudget LocLoc

P1P1 InstrumentationInstrumentation 3.5M3.5M LahoreLahore

P2P2 Database Dev.Database Dev. 2.3M2.3M RawalpindiRawalpindi

P3P3 CAD/CAMCAD/CAM 1.9M1.9M RawalpindiRawalpindi

P4P4 MaintenanceMaintenance 1.6M1.6M PeshawarPeshawar

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Derived Horizontal Derived Horizontal Fragmentation(DHF)Fragmentation(DHF)Derived Horizontal Derived Horizontal

Fragmentation(DHF)Fragmentation(DHF)

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

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• Two important points:Two important points:– Each link is an equi-join.Each link is an equi-join.

– Equijoin can be implemented by means Equijoin can be implemented by means of semi-joinsof semi-joins

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

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RRii = R = R ⋉⋉ S Sii, 1, 1≤ i ≤ w≤ i ≤ w where w is the maximum number of where w is the maximum number of

fragments that will be defined on R and fragments that will be defined on R and

Si = Si = FiFi (S), where Fi is formula for PHF on (S), where Fi is formula for PHF on SS

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DHF ExampleDHF ExampleDHF ExampleDHF 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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eNoeNo eNameeName titletitle

E1E1 T KhanT Khan Elec EngElec Eng

E2E2 W ShahW Shah Sys AnaSys Ana

E3E3 R DarR Dar Mech EngMech Eng

E4E4 K ButtK Butt ProgrammeProgramme

E5E5 F SahbaiF Sahbai Sys AnaSys Ana

E6E6 A HaqA Haq Elec EngElec Eng

E7E7 S FarhanaS Farhana Mech EngMech Eng

E8E8 M DaudM Daud Sys AnaSys Ana

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TitleTitle SalSal

Elect. EngElect. Eng 4000040000

Sys AnalystSys Analyst 3400034000

Mech. EngMech. Eng 2700027000

ProgrammerProgrammer 2400024000

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E3E3 R DarR Dar Mech EngMech Eng

E4E4 K ButtK Butt ProgrammeProgramme

E7E7 S FarhanaS Farhana Mech EngMech Eng

eNoeNo eNameeName titletitle

E1E1 T KhanT Khan Elec EngElec Eng

E2E2 W ShahW Shah Sys AnaSys Ana

E5E5 F SahbaiF Sahbai Sys AnaSys Ana

E6E6 A HaqA Haq Elec EngElec Eng

E8E8 M DaudM Daud Sys AnaSys Ana

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