Broadcast gossip algorithms: Design and analysis for consensus

Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we have recently proposed a broadcasting-based gossiping protocol to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. The class of broadcast gossip algorithms achieve consensus almost surely at a value that is in the neighborhood of the initial node measurements¿ average. In this paper, we further study the broadcast gossip algorithms: we derive and analyze the optimal mixing parameter of the algorithm when approached from worst-case convergence rate, present theoretical results on limiting mean square error performance of the algorithm, and find the convergence rate order of the proposed protocol.

[1]  Alexandros G. Dimakis,et al.  Geographic Gossip: Efficient Averaging for Sensor Networks , 2007, IEEE Transactions on Signal Processing.

[2]  Anand D. Sarwate,et al.  Broadcast Gossip Algorithms for Consensus , 2009, IEEE Transactions on Signal Processing.

[3]  Panganamala Ramana Kumar,et al.  Toward a theory of in-network computation in wireless sensor networks , 2006, IEEE Communications Magazine.

[4]  Asuman E. Ozdaglar,et al.  Convergence rate for consensus with delays , 2010, J. Glob. Optim..

[5]  Johannes Gehrke,et al.  Gossip-based computation of aggregate information , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[6]  P. Kumar,et al.  Towards a Theory of In-Network Computation in Wireless Sensor Networks , 2006 .

[7]  Stephen P. Boyd,et al.  A scheme for robust distributed sensor fusion based on average consensus , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[8]  John N. Tsitsiklis,et al.  On distributed averaging algorithms and quantization effects , 2007, 2008 47th IEEE Conference on Decision and Control.

[9]  M. Rabbat,et al.  Rates of Convergence for Distributed Average Consensus with Probabilistic Quantization , 2007 .

[10]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[11]  Mehmet E. Yildiz,et al.  Broadcast gossip algorithms , 2008, 2008 IEEE Information Theory Workshop.

[12]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[13]  N. Alon,et al.  il , , lsoperimetric Inequalities for Graphs , and Superconcentrators , 1985 .

[14]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[15]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[16]  John N. Tsitsiklis,et al.  Problems in decentralized decision making and computation , 1984 .

[17]  Benjamin Van Roy,et al.  Consensus Propagation , 2005, IEEE Transactions on Information Theory.

[18]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[19]  Alexandros G. Dimakis,et al.  Order-Optimal Consensus Through Randomized Path Averaging , 2010, IEEE Transactions on Information Theory.