TY - GEN

T1 - An upper bound on the convergence time for quantized consensus

AU - Shang, Shang

AU - Cuff, Paul

AU - Hui, Pan

AU - Kulkarni, Sanjeev

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Distributed quantized consensus

KW - convergence time

KW - gossip

UR - http://www.scopus.com/inward/record.url?scp=84883089141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883089141&partnerID=8YFLogxK

U2 - 10.1109/INFCOM.2013.6566843

DO - 10.1109/INFCOM.2013.6566843

M3 - Conference contribution

AN - SCOPUS:84883089141

SN - 9781467359467

T3 - Proceedings - IEEE INFOCOM

SP - 600

EP - 604

BT - 2013 Proceedings IEEE INFOCOM 2013

T2 - 32nd IEEE Conference on Computer Communications, IEEE INFOCOM 2013

Y2 - 14 April 2013 through 19 April 2013

ER -