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A Blueprint for Constructing Peer-to-Peer Systems Robust to Dynamic Worst-Case Joins and Leaves

This paper presents techniques for building and maintaining Peer-to-Peer systems that are robust to ongoing worst-case membership changes. It introduces a model for dynamics and explores a topology maintenance approach to ensure a stable and efficient P2P network under churn.

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A Blueprint for Constructing Peer-to-Peer Systems Robust to Dynamic Worst-Case Joins and Leaves

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  1. A Blueprint for Constructing Peer-to-Peer Systems Robust to Dynamic Worst-Case Joins and Leaves Fabian Kuhn, Microsoft Research, Silicon Valley Stefan Schmid, ETH Zurich Joest Smit, ETH Zurich Roger Wattenhofer, ETH Zurich 14th IEEE Int. Workshop on Quality of Service (IWQoS) Yale University, New Haven, CT, USA, June 2006

  2. Brief Intro to Peer-to-Peer Computing (1) P2P computing = power by accumulating distributed resources (CPU cycles, disk space, …) Peer-to-Peer • Decentralized („all machines“) • Scalable • Efficient • … Client / Server • Centralized („one machine“) • Bottleneck • Single Point of Failure • … vs Stefan Schmid, ETH Zurich @ IWQoS 2006

  3. Brief Intro to Peer-to-Peer Computing (2) • Examples: - computing power (Folding@Home, …) - file sharing (eMule, Kangoo, …) - internet telephony (Skype, …) - media streaming (Swistry, …) distributed computations file sharing Swistry (live media streaming) Stefan Schmid, ETH Zurich @ IWQoS 2006

  4. Churn (1) • But: unlike server, peers are transient! • Machines under control of individual users • E.g., just connecting to download one file • Membership changes are called churn Successful P2P systems have to cope with churn (i.e., guarantee correctness, efficiency, etc.)! Stefan Schmid, ETH Zurich @ IWQoS 2006

  5. Dynamic resources: A challenge in P2P computing! Churn (2) • Churn characteristics: • Depends on application (Skype vs. eMule vs. …) • But: There may be dozens of membership changes per second! • Peers may crash without notice! How can peers collaborate in spite of churn? Stefan Schmid, ETH Zurich @ IWQoS 2006

  6. Churn (3) • Churn is important, as it threatens “advantages of P2P computing”! a lot of churn We have to activelymaintain P2P systems! Stefan Schmid, ETH Zurich @ IWQoS 2006

  7. Our Paper… Unfortunately, only few P2P systems have been analyzed under churn! Our paper… Peer degree, network diameter, … … presents techniques to: - … build and provably maintain P2P systems with desirable properties… - … in spite of ongoing worst-case membership changes. „adversary“ non-stop attacks weakest part (system „never fully repaired, but always fully functional“) Stefan Schmid, ETH Zurich @ IWQoS 2006

  8. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  9. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  10. Model for Dynamics • Churn = possibly concurrent membership changes, at any time! • We assume worst-case perspective: Adversary ADV(J,L) • i.e., joins and leaves may take place at the weakest spot of the network • Synchronous model: time divided into rounds (e.g., max round trip time) time ADV(J,L): In each round, at most J peers may joins and at most L peers leave (crash). Stefan Schmid, ETH Zurich @ IWQoS 2006

  11. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  12. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  13. Topology Maintenance • An efficient P2P topology under churn: π1 π2 • Almost impossible to maintain the hypercube! • How does peer 1 know that it should replace peer 2? • How does it get there when there are concurrent joins and leaves? • … Is there a more robust topology but with same small degree and diameter? Stefan Schmid, ETH Zurich @ IWQoS 2006

  14. Simple idea: Simulate the topology! Our Approach Stefan Schmid, ETH Zurich @ IWQoS 2006

  15. Resulting structure has similar properties as original graph (e.g., connectivity, degree, …), but is also maintainable under churn! There is always at least one peer per node (but not too many either). General Recipe for Robust Topologies • Take a graph with desirable properties • Low diameter, low peer degree, etc. • Replace vertices by a set of peers 3. Maintain it: a. Permanently run a peer distribution algorithm which ensures that all vertices have roughly the same amount of peers (“token distribution algorithm”). b. Estimate the total number of peers in the system and change “dimension of topology” accordingly (“information aggregation algorithm” and “scaling algorithm”). Stefan Schmid, ETH Zurich @ IWQoS 2006

  16. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  17. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  18. The Pancake Graph (1) • A robust system with degree and diameter O(log n / loglog n): the pancake graph • E.g., Papadimitriou & Gates! • Pancake of dimension d: • d! nodes represented by unique permutation {l1, …, ld} of set {1,…,d} • Two nodes u and v are adjacent iff u is a prefix-inversion of v 1234 4321 4-dimensional pancake: 3214 2134 Stefan Schmid, ETH Zurich @ IWQoS 2006

  19. No other graph can have a smaller degree and a smaller diameter! The Pancake Graph (2) • Properties • Node degree Θ (log n / loglog n) • Diameter Θ (log n / loglog n) • … where n is the total number of nodes • A factor loglog n better than hypercube! • But: difficult graph (diameter unknown!) Stefan Schmid, ETH Zurich @ IWQoS 2006

  20. Contribution • Using peer distribution and information aggregation algorithms… • … on the simulated pancake topology, we can construct: • a peer-to-peer system (“distributed hash table”) with • Peer degree and lookup / network diameter in Θ (log n / loglog n) • Robustness to ADV(Θ (log n / loglog n), Θ (log n / loglog n)) • No data is ever lost! Asymptotically optimal! Stefan Schmid, ETH Zurich @ IWQoS 2006

  21. The Pancake System Stefan Schmid, ETH Zurich @ IWQoS 2006

  22. Stefan Schmid, ETH Zurich @ IWQoS 2006

  23. Both happens concurrently to ongoing churn! If fast enough, pancake is maintained! Basic Components • Peer Distribution Algorithm • Balance peers between neighboring nodes • One (pancake-) dimension after the other! • Information Aggregation Algorithm • Exploit recursive structure of pancake • Aggregate „sub-pancakes“ with increasing order Always at least one peer per node! Stefan Schmid, ETH Zurich @ IWQoS 2006

  24. Inside node, peers have to form a grid! Internals (1) How are peers connected in the simulated topology? Idea: Matching Clique Clique • Problem: • There are up to Θ ((log n / loglog n)2) many peers in each node • Clique would render peer degree too large! Stefan Schmid, ETH Zurich @ IWQoS 2006

  25. Internals (2) Solution: Matching Grid Grid • Each peer is connected to all peers which are either in the same row or column • Degree is OK now, and still robust enough to churn! Stefan Schmid, ETH Zurich @ IWQoS 2006

  26. Internals (3) • “Distributed Hash Table”: • Stores data at nodes • But on which peers of node of given ID? • On just one is bad in dynamic enviroment! • All? • Possible! • But much data movement during peer distribution. • Better idea: • Peers of a node fall into two categories: Protons and Electrons • Protons = „core peers“, store data, are „seldom“ used during token distribution • Electrons = „peripheral peers“, do not store data, are used for balancing • Make sure that there are always enough protons (no data loss)! Stefan Schmid, ETH Zurich @ IWQoS 2006

  27. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  28. Talk Outline • A model for dynamics • Overview of techniques • Example: A robust system with degree and diameter O(log n / loglog n) • Conclusion Stefan Schmid, ETH Zurich @ IWQoS 2006

  29. Conclusion • Contribution: A scheme to maintainquality of a peer-to-peer system in spite of worst-case membership changes. • Ingredients: “base graph”, token distribution & information aggregation algorithm • Proofs possible! • Simulated graph can have similar properties as base graph. • Degree, diameter, etc. • May require some additional thinking, though! (e.g., grid) • A peer-to-peer system with degree and diameter in O(log n/loglog n) which tolerates O(log n/loglog n) joins and leaves per round. • Better than often-used hypercube graph! • But: difficult graph! (e.g., dimension change) • Open questions • How to coordinate dynamic peers or resources: An exciting field of research! • E.g.: Self-stabilization, dirty leaves, etc. Stefan Schmid, ETH Zurich @ IWQoS 2006

  30. Questions and Feedback? Thank you for your attention! Stefan Schmid Distributed Computing Group schmiste@ethz.ch http://dcg.ethz.ch/members/stefan.html Stefan Schmid, ETH Zurich @ IWQoS 2006

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