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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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  1. 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

  2. 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

  3. Peer-to-Peer Data-Sharing System

  4. 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

  5. Alternative Semantics for Mapping Tables • Closed-Closed-World Semantics • Closed-Open-World Semantics

  6. 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

  7. Mapping Constraint Mapping table m Relation GDB Relation SwissProt • Mapping Constraint A relation having attributes from both GDB and SwissProt

  8. 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)

  9. 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(’)

  10. Example of Cover  ={1, 2} Relation r1 Relation r3 Relation r2 Mapping table m Mapping table m1 Mapping table m2

  11. 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 

  12. 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

  13. 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}

  14. 1 2 3 4 Partitions µ2 µ4 µ6 µ1 µ3 µ5

  15. 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

  16. 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.

  17. Description of the Algorithm • The algorithm has two phases • The Information gathering Phase • The Computation Phase

  18. 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

  19. 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

  20. 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.

  21. Thank You

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