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Mapping Data in Peer-to-Peer Systems: Semantics and Algorithmic Issues By A. Kementsietsidis, M. Arenas and R.J. Miller Presented by Md. Anisur Rahman: Anahit Martirosyan: LianXiang Qiu: University Of Ottawa Winter 2004

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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

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Peer-to-Peer Data-Sharing System

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What is a Mapping Table? GDB_idSwissProt_id G1 G2 G3 P9 Q62 P40 P38 GDB_idGene_Name G1 G2 G3 NF1 NF2 NGFB SwissProt_idProtein_ name P9 P40 NF1 MERL Relation GDB Relation SwissProt 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

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Alternative Semantics for Mapping Tables Closed-Closed-World Semantics Closed-Open-World Semantics GDB_idSwissProt_id G2P40 GDB_idSwissProt_id G2 v - {G2} P40 v’ - {P40}

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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 Attr1Attr2 a3 b2 v-{a,b}1 dom(Attr1)={a, b, c, d} dom(Attr2)={1, 2, 3} p(a) = a p(3) = 3 p(v) = c p(v) = d Mapping table m

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Mapping Constraint GDB_idGene_Name G1 G2 G3 NF1 NF2 NGFB SwissProt_idProtein_ name P9 P40 NF1 MERL GDB_idSwissProt_id G2 v - {G2} P40 v’ - {P40} Relation GDB Relation SwissProt GDB_idGENE_NameSwissprot_idProtein_ Name G1 G2 G3 G2 NF1 NF2 NGFB NF2 P9 P40 P9 NF1 MERL NF1 Mapping table m A relation having attributes from both GDB and SwissProt Mapping Constraint

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Extension of a mapping constraint Given a mapping constraint ext ( ) = { (t) | t m and is a valuation over m } Attr1Attr2 a3 b2 v-{a,b}1 Mapping table m dom(Attr1)={a, b, c, d} dom(Attr2)={1, 2, 3} Attr1Attr2 a3 b2 c1 d1 ext(µ)

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A mapping constraint is 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( ’) Cover of a set of mapping constraints

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Example of Cover B1B1 B2B2 px1 qy2 rz3 rx4 A1A1 A2A2 B1B1 pxpx qyqy v-{p,q}v’ v’’-{px,qy} C1C1 C2C2 ai bj ck A1A1 A2A2 px qy rz B1B1 C1C1 C2C2 pxai qybj v-{px,qy} v’v’’-{I,j} A1A1 A2A2 C1C1 C2C2 pxai qybj Mapping table m 1 Mapping table m 2 Mapping table m Relation r 1 Relation r 2 Relation r 3 ={ 1, 2 }

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The Algorithm Input A path = P 1, P 2,…., P n of peers A set of mapping constraints over path Two sets of attributes X and Y in peers P 1 and P n Output: A mapping constraint that is a cover of

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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

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An Example P1P1 P3P3 =P 1, P 2, P 3, P 4 = {µ 1, µ 2,…, µ 11 } {A 1, A 2,.., A 6 } P2P2 {B 1, B 2,.., B 6 } {C 1,C 2,C 3,C 4 } P4P4 {D 3, D 4 }

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Partitions µ2µ2 µ1µ1 µ3µ3 µ5µ5 µ4µ4 µ6µ6 11 22 33 44

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Inferred Partitions Peer P 1 Peer P 2 11 22 33 44 55 66 77 11 55 22 66 33 77 44 Inferred partition over P 1 and P 2

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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.

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

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Information Gathering Phase P1P1 P2P2 P3P3 P4P4 Compute partitions For each partition send to P 2 the set of attributes in the partition Compute own partitions Compute inferred partitions using the information of partitions of P 1 Compute own partitions Compute inferred partitions using the information of propagated inferred partitions from P 2

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Computation Phase P1P1 P2P2 P3P3 P4P4 Using the local constraints of the inferred partition, computes a cover between P 3 and P 4 The mappings belonging to the cover are streamed to peer P 2. 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 P 4 Uses the incoming stream of mappings to generate a cover between its own attributes and those of peer P 4

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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.

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Thank You

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