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Mapping Data in Peer-to-Peer Systems: Semantics and Algorithmic Issues B y A. Kementsietsidis, M. Arenas and R.J. Miller Presented by Md. Anisur Rahman: 3558643 Anahit Martirosyan: 100628480 LianXiang Qiu: 3603336 University Of Ottawa Winter 2004. Outline. P2P Data-Sharing-System

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Mapping Data in Peer-to-Peer Systems: Semantics and Algorithmic IssuesBy A. Kementsietsidis, M. Arenas and R.J. MillerPresented by Md. Anisur Rahman: 3558643Anahit Martirosyan: 100628480LianXiang Qiu: 3603336University Of OttawaWinter 2004

outline
Outline
  • P2P Data-Sharing-System
  • Mapping Table
  • Alternative Semantics for Mapping Tables
  • Mapping Tables as Constraints
  • An algorithm for checking consistency of the existing mappings and inferring new mappings from them
  • Conclusion and Future work
what is a mapping table
What is a Mapping Table?

Relation SwissProt

Relation GDB

Mapping Table

  • A mapping table m from a set of attributes X to a set of attributes Y is a finite set of mappings over X  Y
alternative semantics for mapping tables
Alternative Semantics for Mapping Tables
  • Closed-Closed-World Semantics
  • Closed-Open-World Semantics
valuation over a mapping table
Valuation over a mapping table
  • A valuation p over mapping table m is a function that maps
    • each constant value in m to itself and
    • each variable v of m to a value of the domain of the attribute where v appears
  • If v appears in the expression of the form v-S , then p(v)S

p(a) = a

p(3) = 3

p(v) = c

p(v) = d

dom(Attr1)={a, b, c, d}

dom(Attr2)={1, 2, 3}

Mapping table m

mapping constraint
Mapping Constraint

Mapping table m

Relation GDB

Relation SwissProt

  • Mapping Constraint

A relation having attributes from both GDB and SwissProt

extension of a mapping constraint
Extension of a mapping constraint
  • Given a mapping constraint

ext () = {(t) |t mand is a valuation over m}

dom(Attr1)={a, b, c, d}

dom(Attr2)={1, 2, 3}

Mapping table m

ext(µ)

cover of a set of mapping constraints
Cover of a set of mapping constraints
  • A mapping constraintis called the cover of a set of mapping constraints  if
    •  is consistent if and only if there exists text()
    • For every mapping constraint , ╞’ if and only if ext()  ext(’)
example of cover
Example of Cover

 ={1, 2}

Relation r1

Relation r3

Relation r2

Mapping table m

Mapping table m1

Mapping table m2

the algorithm
The Algorithm
  • Input
    • A path  = P1, P2,…., Pn of peers
    • A set  of mapping constraints over path 
    • Two sets of attributes X and Y in peers P1 and Pn
  • Output:
    • A mapping constraint that is a cover of 
how is the algorithm useful
How is the Algorithm useful?
  • To check whether ╞’
    • Run the algorithm to find the cover 
    • Check whether ext()  ext(’).
  • To check whether is consistent
    • Run the algorithm to find the cover 
    • Check whether ext() is nonempty
an example

P2

P4

{B1, B2,.., B6}

{D3, D4}

An Example

P1

P3

{C1,C2,C3,C4}

{A1, A2,.., A6}

 =P1, P2, P3, P4

 = {µ1, µ2,…, µ11}

partitions

1

2

3

4

Partitions

µ2

µ4

µ6

µ1

µ3

µ5

inferred partitions

5

1

6

7

2

3

4

Inferred Partitions

Peer P1

Peer P2

Inferred partition over

P1 and P2

3

1

5

6

7

2

4

advantages of partitioning
Advantages of Partitioning
  • While computing the cover, partitioning reduces computational cost as fewer constraints are considered at a time.
  • Different partitions can be processed in parallel.
description of the algorithm
Description of the Algorithm
  • The algorithm has two phases
    • The Information gathering Phase
    • The Computation Phase
information gathering phase
Information Gathering Phase

P1

P2

P3

P4

  • Compute own partitions
  • Compute inferred partitions using the information of propagated inferred partitions from P2
  • Compute own partitions
  • Compute inferred partitions using the information of partitions of P1
  • Compute partitions
  • For each partition send to P2 the set of attributes in the partition
computation phase
Computation Phase

P1

P2

P3

P4

  • Using the local constraints of the inferred partition , computes a cover between P3 and P4
  • The mappings belonging to the cover are streamed to peer P2.
  • Determines with which of its own partitions the incoming stream of mapping should be associated
  • With this information it generates a cover between itself and P4
  • Uses the incoming stream of mappings to generate a cover between its own attributes and those of peer P4
conclusion and future scope
Conclusion and Future Scope
  • This paper showed that by treating mapping tables as constraints on the exchange of information between peers it is possible to reason about them and check their consistency.
  • There is scope for investigating the use of mapping tables in support of query answering.