Broadcast gossip algorithms for consensus

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

Research output: Contribution to journalArticlepeer-review

360 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2748-2761
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number7
StatePublished - 2009
Externally publishedYes


  • Broadcasting
  • Distributed average consensus
  • Gossip algorithms
  • Sensor networks

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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