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Brief Announcement: Practical Summation via Gossip

Brief Announcement: Practical Summation via Gossip. Wesley W. Terpstra, Christof Leng, Alejandro P. Buchmann Databases and Distributed Systems Group Technische Universität Darmstadt Germany. Sum calculation in peer-to-peer. Input: every peer has a value Output: (at least) one peer knows

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Brief Announcement: Practical Summation via Gossip

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  1. Brief Announcement:Practical Summation via Gossip Wesley W. Terpstra, Christof Leng, Alejandro P. Buchmann Databases and Distributed Systems Group Technische Universität Darmstadt Germany

  2. Sum calculation in peer-to-peer • Input: every peer has a value • Output: (at least) one peer knows • Useful in computing many global statistics: • Network size • Average utilization • Load balance (standard deviation) • Churn (rate of peer replacement) • Size of stored data For our system, BubbleStorm, we compute  degi(p)

  3. Build on an existing solution • Approaches can be compared by • Message rounds (latency) • Total messages (bandwidth) • Parameters: system size (n), accuracy () • We improve the Push-Sum algorithm for practical use

  4. Analogy: Measuring a lake’s volume

  5. Push-Sum visualized

  6. Stationary Distribution (Steady State) Equilibrium: edges carry the same water and fish in both directions peers have water and fish proportional to degree and clock Perturbations of equilibrium do not affect water/fish ratio

  7. Improvement: Big Fish eat smaller fish

  8. Fish eating in the Network

  9. Stationary Distribution (Steady State)

  10. Other improvements • Round switching • Once the result is accurate “enough”, restart • Provides a running estimate on network statistics • Compensate for message loss • Prevent adding two of the most aggressive fish • Save bandwidth for multiple measurements

  11. Synchrony • Kempe et al. prove correctness with synchronous model, but conjecture that it works asynchronously • We validate this claim by simulation • 1 million peers, 5s gossip interval, find network size:

  12. Open Problem • Push-Sum is very vulnerable to attack • Any peer can completely change the result • This is largely due to the problem statement (sum!) • Simplistic prevention (bounds) easily defeated • Introduce too few of the largest fish type  too large • Switch rounds prematurely  too small & unstable • What is a useful adversary model for summation?

  13. Thanks for listening!

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