Broadcast Gossip Algorithms for Consensus
Aysal, T.C.
Yildiz, M.E.
Sarwate, A.D.
Scaglione, A.
Commun. Res. in Signal Process. Group, Cornell Univ., Ithaca, NY;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: July 2009
Volume: 57,
Issue: 7
On page(s): 2748-2761
ISSN: 1053-587X
INSPEC Accession Number: 10704909
Digital Object Identifier: 10.1109/TSP.2009.2016247
First Published: 2009-02-24
Current Version Published: 2009-06-16
Abstract
Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcasting-based gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcastgossipalgorithm converges almost surely to a consensus. We prove that the random consensus value is, in expectation, the average of initial node measurements and that it can be made arbitrarily close to this value in mean squared error sense, under a balanced connectivity model and by trading off convergence speed with accuracy of the computation. We provide theoretical and numerical results on the mean square error performance, on the convergence rate and study the effect of the ldquomixing parameterrdquo on the convergence rate of the broadcast gossip algorithm. The results indicate that the mean squared error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithm to achieve a given distance to consensus through theoretical and numerical results.
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