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Geographic Gossip: Efficient Aggregations for Sensor Networks

Geographic Gossip: Efficient Aggregations for Sensor Networks. Author: Alex Dimakis, Anand Sarwate, Martin Wainwright University: UC Berkeley Venue: IPSN 2006 Presentatior: Yunhuai LIU. Outline. Introduction Proposed algorithm Analysis Conclusion. Distributed Aggregation. 2. 2.

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Geographic Gossip: Efficient Aggregations for Sensor Networks

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  1. Geographic Gossip: Efficient Aggregations for Sensor Networks Author: Alex Dimakis, Anand Sarwate, Martin WainwrightUniversity: UC BerkeleyVenue: IPSN 2006Presentatior: Yunhuai LIU

  2. Outline • Introduction • Proposed algorithm • Analysis • Conclusion

  3. Distributed Aggregation 2 2 • Every node has a measurement (e.g sensing temperature) • Every node wants to access the global average • Want a truly distributed, localized and robust algorithm to compute the average. 3 5 Goal: every node gets (2+2+3+5+12)/5=4.8 with the minimized energy cost 12

  4. Gossip Algorithms for Aggregations 2 2 2.5 • Start with initial measurement as an estimate for the average and update • Each node interacts with a random neighbor and both compute pairwise average (one update) • Converges to true average • Useful building block for more complex problems 3 2.5 3.75 5 3.75 7.87 12 7.87

  5. How Many Interactions ? • ε-averaging time Tave(n, ε): First time where x(k) is ε-close to the normalized true average with probability greater than 1-ε. • Averaging time connected with mixing time • Cost: Number of radio transmissions (fixed Tr radius) The physical meaning of Tave(n, ε): after Tave rounds, with very low probability the difference between the obtained value and the true value is high.

  6. Cost of Standard Gossip • Depends on graph and the transition probabilities: • Complete graph: Tmix=Θ(1)  Tave=Θ(n log(n)) • Small World/Expander: Tmix=Θ(log(n))  Tave=Θ(n log(n)) • Random Geometric Graph: Tave=Θ(n2)

  7. Outline • Introduction • Proposed algorithm • Analysis • Conclusion

  8. Basic Idea of Geographic Gossip • In standard gossip algorithms useful information performs random walks, which diffuses slowly • Basic idea: add a random direction to gossip in order to diffuse faster. • Assume: • Given location information • round-based, i.e., there is a virtual, global clock tick so that in each tick just one node active and conduct pairwise update. • The transmission range r follows:

  9. Random Target Routing • Node picks a random location (=“target”) • Greedy routing towards the target • Perform pairwise update between the source and destination nodes

  10. Geographic Gossip 2.5 2 • Nodes use random routing to gossip with nodes far away in the network • Each interaction costs • But faster mixing (convergence) 2.5 3

  11. Geographic Gossip • When • Expected averaging cost of • w.h.p. the averaging cost is bounded by • The expected averaging cost of

  12. Outline • Introduction • Proposed algorithm • Analysis • Conclusion

  13. Some Interesting Things • How we uniformly randomly select a target node to perform pairwise updates • Rejection sampling technique • When the application field is partitioned by squares with length of with high probability each square contains at least one node. • It equals the probability that nlogn balls are thrown randomly to cover n bins • Averaging algorithms based on pairwise updates have the convergence rate determined by the second largest eigenvalueλ2(W) of the matrix

  14. Outline • Introduction • Proposed algorithm • Analysis • Conclusion

  15. Conclusions • Geographic gossip saves a factor of n1/2 in energy required for aggregation. For realistic graph topologies • Achieves with location information. Only localized distributed operations. distributed, localized, robust. • Can be combined with other related consensus algorithms

  16. Why I Choose This Paper • Learn more about therandom walk based algorithms • How others give analysis • How to apply mathematics in research studies • Eigenvalue in convergence for optimization problems • How others study the issue • Start from real applications: aggregations in WSNs • Narrow down the research domain to a specific problem: get the global average for each node with minimized energy cost • Proposal an algorithm to tackle the problem • Show the effectiveness of the algorithm as deep as possible: depth >> breadth (this is your contribution) • Do not involve too many things; make reasonable assumptions as many as possible to walk around those un-related things

  17. Thanks • Qeuestion and Answer

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