An upper bound on the convergence time for quantized consensus

Shang Shang, Paul Cuff, Pan Hui, Sanjeev Kulkarni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

We analyze a class of distributed quantized consensus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimate by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We start the analysis with a special case of a distributed binary voting algorithm, then proceed to the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N3 log N) upper bound for the expected convergence time on an arbitrary graph of size N, improving on the state of art bound of O(N4 log N) for binary consensus and O(N 5) for quantized consensus algorithms. Our result is not dependent on the graph topology. Simulations are performed to validate the analysis.

Original languageEnglish (US)
Title of host publication2013 Proceedings IEEE INFOCOM 2013
Pages600-604
Number of pages5
DOIs
StatePublished - Sep 2 2013
Event32nd IEEE Conference on Computer Communications, IEEE INFOCOM 2013 - Turin, Italy
Duration: Apr 14 2013Apr 19 2013

Publication series

NameProceedings - IEEE INFOCOM
ISSN (Print)0743-166X

Other

Other32nd IEEE Conference on Computer Communications, IEEE INFOCOM 2013
CountryItaly
CityTurin
Period4/14/134/19/13

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Electrical and Electronic Engineering

Keywords

  • Distributed quantized consensus
  • convergence time
  • gossip

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    Shang, S., Cuff, P., Hui, P., & Kulkarni, S. (2013). An upper bound on the convergence time for quantized consensus. In 2013 Proceedings IEEE INFOCOM 2013 (pp. 600-604). [6566843] (Proceedings - IEEE INFOCOM). https://doi.org/10.1109/INFCOM.2013.6566843