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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

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