Convergence of Gossip Algorithms for Consensus in Wireless Sensor Networks with Intermittent Links and Mobile Nodes

We study the convergence of pairwise gossip algorithmsand broadcast gossip algorithms for consensus withintermittent links and mobile nodes. By nonnegative matrixtheory and ergodicity coefficient theory, we prove gossip algorithmssurely converge as long as the graph is partitionallyweakly connected...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (2014), p.1-18
Main Authors: Bai, Xu, Hou, Yuguan, Zhang, Jiayan, Wu, Shaochuan
Format: Article
Language:English
Subjects:
Algorithms
Broadcasting
Coefficients
Convergence
Cost analysis
Economic models
Eigenvalues
Error analysis
Errors
Graph theory
Graphs
Links
Mathematical analysis
Matrix theory
Nodes
Studies
Theory
Wireless sensor networks
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Summary:We study the convergence of pairwise gossip algorithmsand broadcast gossip algorithms for consensus withintermittent links and mobile nodes. By nonnegative matrixtheory and ergodicity coefficient theory, we prove gossip algorithmssurely converge as long as the graph is partitionallyweakly connected which, in comparison with existing analysis, isthe weakest condition and can be satisfied for most networks. In addition we characterize the supremum for the mean squarederror of convergence as a function associated with the initial statesand the number of nodes. Furthermore, on the condition that thegraph is partitionally strongly connected, the rate of convergenceis proved to be exponential and governed by the second largesteigenvalue of expected coefficient matrix. For partitionally stronglyconnected digraphs, simulation results illustrate that gossipalgorithms actually converge, and broadcast gossip algorithmscan converge faster than pairwise gossip algorithms at the costof larger error of convergence.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/836584