Fast Decentralized Averaging via Multi-scale Gossip

  • Konstantinos I. Tsianos
  • Michael G. Rabbat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6131)


We are interested in the problem of computing the average consensus in a distributed fashion on random geometric graphs. We describe a new algorithm called Multi-scale Gossip which employs a hierarchical decomposition of the graph to partition the computation into tractable sub-problems. Using only pairwise messages of fixed size that travel at most \(O(n^{\frac{1}{3}})\) hops, our algorithm is robust and has communication cost of O(n loglogn logε − 1) transmissions, which is order-optimal up to the logarithmic factor in n. Simulated experiments verify the good expected performance on graphs of many thousands of nodes.


Sensor Network Wireless Sensor Network Communication Cost Hierarchy Level Multiscale Approach 
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  1. 1.
    Tsitsiklis, J.: Problems in Decentralized Decision Making and Computation. PhD thesis, Massachusetts Institute of Tech. (November 1984)Google Scholar
  2. 2.
    Kempe, D., Dobra, A., Gehrke, J.: Computing aggregate information using gossip. In: Proc. Foundations of Computer Science, Cambridge, MA (October 2003)Google Scholar
  3. 3.
    Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Trans. Inf. Theory 52(6), 2508–2530 (2006)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Benezit, F., Dimakis, A., Thiran, P., Vetterli, M.: Gossip along the way: Order-optimal consensus through randomized path averaging. In: Proc. Allerton Conf. on Comm., Control and Comp., Urbana-Champaign, IL (September 2007)Google Scholar
  5. 5.
    Dimakis, A., Sarwate, A., Wainwright, M.: Geographic gossip: Efficient averaging for sensor networks. IEEE Trans. Signal Processing 56(3), 1205–1216 (2008)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Gupta, P., Kumar, P.R.: Critical power for asymptotic connectivity in wireless networks. In: Stochastic Analysis, Control, Optimization and Applications, Boston, pp. 1106–1110 (1998)Google Scholar
  7. 7.
    Penrose, M.: Random Geometric Graphs. Oxford University Press, Oxford (2003)zbMATHCrossRefGoogle Scholar
  8. 8.
    Cao, M., Spielman, D.A., Yeh, E.M.: Accelerated gossip algorithms for distributed computation. In: Proc. 44th Annual Allerton Conf. Comm., Control and Comp., Monticello, IL (September 2006)Google Scholar
  9. 9.
    Kokiopoulou, E., Frossard, P.: Polynomial filtering for fast convergence in distributed consensus. IEEE Trans. Signal Processing 57(1), 342–354 (2009)CrossRefGoogle Scholar
  10. 10.
    Oreshkin, B., Coates, M., Rabbat, M.: Optimization and analysis of distributed averaging with short node memory. To appear IEEE Trans. Signal Processing (2010)Google Scholar
  11. 11.
    Li, W., Dai, H.: Location-aided fast distributed consensus. IEEE Transactions on Information Theory (2008) (submitted)Google Scholar
  12. 12.
    Jung, K., Shah, D., Shin, J.: Fast gossip through lifted Markov chains. In: Proc. Allerton Conf. on Comm., Control and Comp., Urbana-Champaign, IL (September 2007)Google Scholar
  13. 13.
    Sarkar, R., Yin, X., Gao, J., Luo, F., Gu, X.D.: Greedy routing with guaranteed delivery using ricci flows. In: Proc. Information Processing in Sensor Networks, San Francisco (April 2009)Google Scholar
  14. 14.
    Sarkar, R., Zhu, X., Gao, J.: Hierarchical spatial gossip for multi-resolution representations in sensor networks. In: Proc. of the International Conference on Information Processing in Sensor Networks (IPSN 2007), April 2007, pp. 420–429 (2007)Google Scholar
  15. 15.
    Kim, J.H., West, M., Lall, S., Scholte, E., Banaszuk, A.: Stochastic multiscale approaches to consensus problems. In: Proc. IEEE Conf. on Decision and Control, Cancun (December 2008)Google Scholar
  16. 16.
    Epstein, M., Lynch, K., Johansson, K., Murray, R.: Using hierarchical decomposition to speed up average consensus. In: Proc. IFAC World Congress, Seoul (July 2008)Google Scholar
  17. 17.
    Cattivelli, F., Sayed, A.: Hierarchical diffusion algorithms for distributed estimation. In: Proc. IEEE Workshop on Statistical Signal Processing, Wales (August 2009)Google Scholar
  18. 18.
    Denantes, P., Benezit, F., Thiran, P., Vetterli, M.: Which distributed averaging algorithm should i choose for my sensor network? In: Proc. IEEE Infocom, Phoenix (April 2008)Google Scholar
  19. 19.
    Avin, C., Ercal, G.: On the cover time and mixing time of random geometric graphs. Theoretical Computer Science 380, 2–22 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Margulis, G.: Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators. J. Probl. Inf. Transm. 24(1), 39–46 (1988)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Konstantinos I. Tsianos
    • 1
  • Michael G. Rabbat
    • 1
  1. 1.Department of Electrical and Computer EngineeringMcGill UniversityMontrealCanada

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