Brief Announcement: Convergence Analysis of Scalable Gossip Protocols
We present a simple, deterministic gossip protocol for solving the distributed averaging problem. Each node has an initial value and the objective is for all nodes to reach consensus on the average of these values using only communication between neighbors in the network. We first give an analysis of the protocol in structured networks, namely d-dimensional discrete tori and lattices, and show that in an n node network, the number of rounds required for the protocol to converge to within ε of the average is O(|log(ε)| n 2/ d). We then extend our results to derive upper and lower bounds on convergence for arbitrary graphs based on the dimensions of spanning supergraphs and subgraphs.
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- 1.Salapaka, S., Peirce, A., Dahleh, M.: Analysis of a circulant based preconditioner for a class of lower rank extracted systems. In: Numerical Linear Algebra with Applications, vol. 12, pp. 9–32 (2005)Google Scholar
- 2.Patterson, S., Bamieh, B., El Abbadi, A.: Convergence analysis of scalable gossip protocols. Technical Report 2006-09, Department of Computer Science, University of California, Santa Barbara (2006)Google Scholar
- 3.Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: IEEE Symposium on Foundations of Computer Science, p. 482 (2003)Google Scholar
- 4.Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Gossip algorithms: Design, analysis and applications. In: INFOCOM, vol. 3, pp. 1653–1664 (2005)Google Scholar
- 5.Xiao, L., Boyd, S.: Fast linear iterations for distributed averaging. In: Systems and Control Letters, vol. 53, pp. 65–78 (2005)Google Scholar
- 7.Barooah, P., Hespanha, J.: Graph effective resistances and distributed control: Part ii – electrical analogy and scalability. In: 45th IEEE Conference on Decision and Control (February 2006) (submitted, 2006)Google Scholar