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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 CUHK16th December 2004

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Introduction

What is an Unstructured P2P Network?

Centralized

Decentralized

Structured

Unstructured

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Introduction

Locating Objects in an Unstructured P2P Network

Probing

How to Reduce Probe Count?

No Probing is better than Random Probing

By Replication

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Introduction

Current Replication Strategies

… Implicit

Objective of the Paper:

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

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Introduction

Two Starting Points

Uniform Replication

Proportional Replication

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Paper’s Outline Introduction Model and Problem Statement

Defining an Allocation and the Expected Search Size Bounded Search Size and Insoluble Queries Heterogeneous Capacities and Bandwidth

Allocation Strategies Uniform and Proportional Characterizing Allocations Between Uniform and Proportional

The Square-root Allocation How much we can gain?

Square-root* and Proportional* Allocations Square-root* Allocation Proportional* Allocation

Distributed Replication Path Replication Replication with Sibling-number Memory Replication with Probe Memory Obtaining the Optimal Allocation Simulations

Conclusion

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Today’s Outline Introduction Model and Problem Statement

Defining an Allocation and the Expected Search Size Bounded Search Size and Insoluble Queries Heterogeneous Capacities and Bandwidth

Allocation Strategies Uniform and Proportional Characterizing Allocations Between Uniform and Proportional

The Square-root Allocation How much we can gain?

Square-root* and Proportional* Allocations Square-root* Allocation Proportional* Allocation

Distributed Replication Path Replication Replication with Sibling-number Memory Replication with Probe Memory Obtaining the Optimal Allocation Simulations

Conclusion

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Model & Problem Statementn nodes

capacity ρ

total capacity R = nρ

query rate q = q1 ≥ q2 ≥ … ≥ qm Σqi = 1m distinct data

replica r1 r2 rm Σri = R

allocation p = (r1/R, r2/R, … , rm/R)

allocation strategy: q → p

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Model & Problem Statementn nodes

capacity ρ

total capacity R = nρ

m distinct data

query rate q = q1 ≥ q2 ≥ … ≥ qm

replica r1 r2 rm

allocation p = (r1/R, r2/R, … , rm/R)

bounds for m :

R ≥ m ≥ρ

bounds for pi :

u ≥ pi ≥ ll = 1/Ru = n/R = ρ-1

expected search size:

optimization problem:

Monotonicity:

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Allocation Strategies, Uniform & Proportional

• Minimizes the required maximum search size

• Thus minimizes system resources spent on insoluble queries

• Minimizes maximum utilization rate.

• More relevant when the replication is of copies rather than of pointers

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Allocation Strategies, Uniform & Proportional

Expected Search Size Aq(p)

Uniform

Aq(p) = 1/ρΣ(qi/pi)

= 1/ρΣqim

= m/ρ

Proportional

Aq(p) = 1/ρΣ(qi/pi)

= 1/ρΣ1

= m/ρ

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Allocation Strategies, Characterizing Allocations

Consider space allocations for two items pi, pj and qi, qj

Range of allocation defined by x, 0 < x < 1,

pi/(pi +pj) = x

pj/(pi +pj) = (1-x)

x = qi/(qi +qj) [Proportional] or 0.5 [Uniform]

ESS proportional to qi/x + qj/(1-x) and is convex.

ESSmin occurs at which is independent of p.

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Allocation Strategies, Characterizing Allocations

Consider space allocations for two items pi, pj and qi, qj

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Allocation Strategies, Between Uniform & Prop.

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Allocation Strategies, Between Uniform & Prop.

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Allocation Strategies, Short Conclusion

ESS of Uniform and Proportional Allocation is equal, and is equal to m/ρ

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/ρ.

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

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The Square-root Allocation

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How much can we gain?

For uniform and proportional allocation,

ESS = m/ρ

For Square-root allocation,

ESS = (Σqi1/2)2/ρ

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 = 1If l << 1/m, and gain factor is roughly mu.

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How much can we gain?

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How much can we gain?

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Materials Left

Natural 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 Allocation Path replication, converges but unstable Replication with sibling-number memory, better Replication with probe memory, better Confirmed with Simulation

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Conclusion

Modeled different replication strategies Uniform Proportional In-between, especially Square-root

Uniform and Proportional forms two extremes of all legal allocations

ESS is smaller in-between

Square-root is optimal