Broadcast gossip algorithms for consensus

  • Authors:

  • Tuncer Can Aysal;Mehmet Ercan Yildiz;Anand D. Sarwate;Anna Scaglione

  • Affiliations:

  • School of Electrical and Computer Engineering, Cornell University, Ithaca, NY;School of Electrical and Computer Engineering, Cornell University, Ithaca, NY;Information Theory and Applications Center, University of California at San Diego, La Jolla, CA and Department of Electrical Engineering and Computer Sciences, University of California at Berkeley ...;Electrical and Computer Engineering, University of California, Davis, CA and School of Electrical and Computer Engineering, Cornell University, Ithaca, NY

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2009

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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 broadcast gossip algorithm 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 "mixing parameter" 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.