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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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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, 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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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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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