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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

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

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

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Stefan Schmid, ETH IWQoS 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.)!

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Stefan Schmid, ETH IWQoS Churn (2) Dynamic resources: A challenge in P2P computing! 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?

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Stefan Schmid, ETH IWQoS Churn (3) Churn is important, as it threatens “advantages of P2P computing”! a lot of churn We have to actively maintain P2P systems!

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

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

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

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Stefan Schmid, ETH IWQoS 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).

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

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

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Stefan Schmid, ETH IWQoS Topology Maintenance An efficient P2P topology under churn: π1π1 π2π2 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?

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Stefan Schmid, ETH IWQoS Our Approach Simple idea: Simulate the topology!

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Stefan Schmid, ETH IWQoS General Recipe for Robust Topologies 1.Take a graph with desirable properties -Low diameter, low peer degree, etc. 2.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”). 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).

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

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

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Stefan Schmid, ETH IWQoS 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 {l 1, …, l d } of set {1,…,d} –Two nodes u and v are adjacent iff u is a prefix-inversion of v 4-dimensional pancake:

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Stefan Schmid, ETH IWQoS 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!) No other graph can have a smaller degree and a smaller diameter!

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Stefan Schmid, ETH IWQoS 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!

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Stefan Schmid, ETH IWQoS The Pancake System

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Stefan Schmid, ETH IWQoS

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Stefan Schmid, ETH IWQoS 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 Both happens concurrently to ongoing churn! If fast enough, pancake is maintained! Always at least one peer per node!

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

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Stefan Schmid, ETH IWQoS Internals (2) Solution: Grid Matching 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!

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Stefan Schmid, ETH IWQoS 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)!

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

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

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Stefan Schmid, ETH IWQoS Conclusion Contribution: A scheme to maintain quality 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.

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Stefan Schmid, ETH IWQoS Questions and Feedback? Stefan Schmid Distributed Computing Group Thank you for your attention!

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