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Exploring Mapping Data in Peer-to-Peer Systems: Semantics and Algorithmic Challenges

This paper discusses the challenges and methodologies for mapping data in Peer-to-Peer (P2P) systems. It covers the construction and semantics of mapping tables that facilitate data sharing between peers, with an emphasis on alternative semantics like closed and open-world scenarios. The authors present an algorithm for checking the consistency of existing mappings and inferring new mappings, highlighting the importance of mapping constraints. This analysis aims to improve data exchange efficiency and lays the groundwork for future explorations in P2P query answering systems.

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Exploring Mapping Data in Peer-to-Peer Systems: Semantics and Algorithmic Challenges

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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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