Replication Strategies in Unstructured Peer-to-Peer Networks

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Replication Strategies in Unstructured Peer-to-Peer Networks. Edith Cohen, Scott Shenker ACM SIGCOMM Computer Communication Review, Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications, vol. 32 issue 4 - PowerPoint PPT Presentation

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  • Replication Strategies in Unstructured Peer-to-Peer Networks Edith Cohen, Scott Shenker ACM SIGCOMM Computer Communication Review, Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications, vol. 32 issue 4

    Presentation by Tony Sung, MC Lab, IE CUHK 16th December 2004

  • IntroductionWhat is an Unstructured P2P Network?

    Centralized

    Decentralized

    Structured

    Unstructured

  • IntroductionLocating Objects in an Unstructured P2P Network

    Probing

    How to Reduce Probe Count?

    No Probing is better than Random Probing

    By Replication

  • IntroductionCurrent Replication Strategies

    Implicit

    Objective of the Paper:

    Designs an explicit replication strategy.What is the optimal way to replicate data?

  • IntroductionTwo Starting Points

    Uniform Replication

    Proportional Replication

  • Papers OutlineIntroductionModel and Problem StatementDefining an Allocation and the Expected Search SizeBounded Search Size and Insoluble QueriesHeterogeneous Capacities and BandwidthAllocation StrategiesUniform and ProportionalCharacterizing AllocationsBetween Uniform and ProportionalThe Square-root AllocationHow much we can gain?Square-root* and Proportional* AllocationsSquare-root* AllocationProportional* AllocationDistributed ReplicationPath ReplicationReplication with Sibling-number MemoryReplication with Probe MemoryObtaining the Optimal AllocationSimulationsConclusion

  • Todays OutlineIntroductionModel and Problem StatementDefining an Allocation and the Expected Search SizeBounded Search Size and Insoluble QueriesHeterogeneous Capacities and BandwidthAllocation StrategiesUniform and ProportionalCharacterizing AllocationsBetween Uniform and ProportionalThe Square-root AllocationHow much we can gain?Square-root* and Proportional* AllocationsSquare-root* AllocationProportional* AllocationDistributed ReplicationPath ReplicationReplication with Sibling-number MemoryReplication with Probe MemoryObtaining the Optimal AllocationSimulationsConclusion

  • Model & Problem Statementallocation strategy: q p

  • Model & Problem Statementbounds for m : R m bounds for pi : u pi l l = 1/R u = n/R = -1expected search size:

    optimization problem:

    Monotonicity:

  • Allocation Strategies, Uniform & Proportional

  • Allocation Strategies, Uniform & ProportionalExpected Search Size Aq(p)UniformAq(p)= 1/(qi/pi)= 1/qim= m/ProportionalAq(p)= 1/(qi/pi)= 1/1= m/

  • Allocation Strategies, Characterizing AllocationsConsider space allocations for two items pi, pj and qi, qj

  • Allocation Strategies, Characterizing AllocationsConsider space allocations for two items pi, pj and qi, qj

  • Allocation Strategies, Between Uniform & Prop.

  • Allocation Strategies, Between Uniform & Prop.

  • Allocation Strategies, Short ConclusionESS of Uniform and Proportional Allocation is equal, and is equal to m/

    For one special case (m=2), ESS is a convex function and is minimum for a square-root allocation

    For any allocation p that lies between Uniform and Proportional, its ESS is at most m/.

    If p is different from Uniform or Proportional then its ESS is strictly less than m/.

  • The Square-root Allocation

  • How much can we gain?For uniform and proportional allocation, ESS= m/

    For Square-root allocation, ESS= (qi1/2)2/ which depends on the query distribution

    Define gain factor as ESSuniform/ESSSR It is shown that ESSuniform/ESSSR m(u + l - mlu) When l = 1/m or u = 1/m, the only legal allocation is pi = 1/m, and gain factor = 1 If l

  • How much can we gain?

  • How much can we gain?

  • Materials LeftNatural extension of Square-root and Proportional Allocation that are defined when l is fixed for a maximum search size.Similar Results

    Distributed Replication Protocols for achieving Square-root AllocationPath replication, converges but unstableReplication with sibling-number memory, betterReplication with probe memory, betterConfirmed with Simulation

  • ConclusionModeled different replication strategiesUniformProportionalIn-between, especially Square-root

    Uniform and Proportional forms two extremes of all legal allocations

    ESS is smaller in-between

    Square-root is optimal

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