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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

- 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

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

- Closed-Closed-World Semantics
- Closed-Open-World Semantics

- 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 table m

Relation GDB

Relation SwissProt

- Mapping Constraint

A relation having attributes from both GDB and SwissProt

- 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)

- A mapping constraintis called the cover of a set of mapping constraints if
- is consistent if and only if there exists text()
- For every mapping constraint , ╞’ if and only if ext() ext(’)

={1, 2}

Relation r1

Relation r3

Relation r2

Mapping table m

Mapping table m1

Mapping table m2

- 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

- 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

P2

P4

{B1, B2,.., B6}

{D3, D4}

P1

P3

{C1,C2,C3,C4}

{A1, A2,.., A6}

=P1, P2, P3, P4

= {µ1, µ2,…, µ11}

1

2

3

4

µ2

µ4

µ6

µ1

µ3

µ5

5

1

6

7

2

3

4

Peer P1

Peer P2

Inferred partition over

P1 and P2

3

1

5

6

7

2

4

- While computing the cover, partitioning reduces computational cost as fewer constraints are considered at a time.
- Different partitions can be processed in parallel.

- The algorithm has two phases
- The Information gathering Phase
- The Computation 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

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

- 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.

Thank You