Replication Strategies in Unstructured Peer-to-Peer Networks

1. Replication Strategies in Unstructured Peer-to-Peer Networks Edith Cohen, Scott ShenkerACM 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 December2004

2. Introduction What is an Unstructured P2P Network? • Centralized • Decentralized • Structured • Unstructured

3. Introduction Locating Objects in an Unstructured P2P Network • Probing • How to Reduce Probe Count? • No Probing is better than Random Probing • By Replication

4. Introduction Current Replication Strategies … Implicit Objective of the Paper: “Designs an explicit replication strategy.” “What is the optimal way to replicate data?”

5. Introduction Two Starting Points Uniform Replication Proportional Replication

6. 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

7. 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

8. Model & Problem Statement nnodes capacityρ total capacityR = nρ replica r1 r2 rm Σri= R mdistinct data allocation p = (r1/R, r2/R, … , rm/R) query rate q = q1≥ q2≥ … ≥ qm Σqi= 1 allocation strategy: q → p

9. Model & Problem Statement nnodes capacityρ total capacityR = nρ replica r1 r2 rm mdistinct data query rate q = q1≥ q2≥ … ≥ qm allocation p = (r1/R, r2/R, … , rm/R) bounds for m: R ≥ m ≥ρ bounds for pi: u ≥ pi ≥ ll = 1/R u = n/R = ρ-1 expected search size: optimization problem: Monotonicity:

10. 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

11. 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

12. Allocation Strategies, Characterizing Allocations 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 toqi/x + qj/(1-x) and is convex. ESSminoccurs at which is independent ofp. Consider space allocations for two items pi, pjandqi, qj

13. Allocation Strategies, Characterizing Allocations Consider space allocations for two items pi, pjandqi, qj

14. Allocation Strategies, Between Uniform & Prop.

15. Allocation Strategies, Between Uniform & Prop.

16. 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.

17. The Square-root Allocation

18. How much can we gain? • For uniform and proportional allocation,ESS = m/ρ • For Square-root allocation,ESS = (Σqi1/2)2/ρwhich depends on the query distribution • Define gain factor as ESSuniform/ESSSRIt is shown that ESSuniform/ESSSR ≤ m(u + l - mlu)When l = 1/moru = 1/m, the only legal allocation is pi = 1/m, and gain factor = 1If l << 1/m, and gain factor is roughly mu.

19. How much can we gain?

20. How much can we gain?

21. 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

22. 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