Paper Info
Title
Broadcast Gossip Algorithms for Consensus on Strongly Connected Digraphs
Abstract
We study a general framework for broadcast gossip algorithms which use companion variables to solve the average consensus problem. Each node maintains an initial state and a companion variable. Iterative updates are performed asynchronously whereby one random node broadcasts its current state and companion variables and all other nodes receiving the broadcast update their state and companion variables. We provide conditions under which this scheme is guaranteed to converge to a consensus solution, where all nodes have the same limiting values, on any strongly connected directed graph. Under stronger conditions, which are reasonable when the underlying communication graph is undirected, we guarantee that the consensus value is equal to the average, both in expectation and in the mean-squared sense. Our analysis uses tools from non-negative matrix theory and perturbation theory. The perturbation results rely on a parameter being sufficiently small. We characterize the allowable upper bound as well as the optimal setting for the perturbation parameter as a function of the network topology, and this allows us to characterize the worst-case rate of convergence. Simulations illustrate that, in comparison to existing broadcast gossip algorithms, the approaches proposed in this paper have the advantage that they simultaneously can be guaranteed to converge to the average consensus and they converge in a small number of broadcasts.
Year
DOI
Venue
2012
10.1109/TSP.2013.2264056
IEEE Transactions on Signal Processing
Keywords
DocType
Volume
nonnegative matrix theory,distributed averaging,companion variables,perturbation theory,signal processing,broadcast gossip algorithms,distributed signal processing,matrix algebra,network topology,connected directed graph,communication graph,iterative updates,directed graphs,wireless sensor networks,consensus problem,iterative methods,strongly connected digraphs,random node broadcasts
Journal
61
Issue
ISSN
Citations 
16
1053-587X
16
PageRank 
References 
Authors
0.73
8
2
Name
Order
Citations
PageRank
Shaochuan Wu1186.51
Michael G. Rabbat21631111.76