Convergence time analysis of quantized gossip consensus on digraphs

Authors:
Kai Cai;Hideaki Ishii
Affiliations:
Department of Electrical and Computer Engineering, University of Toronto, 10 King's College Rd, Toronto, M5S 3G4, Canada;Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-J2-54, Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2012

Citing 4
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Abstract

We have recently proposed quantized gossip algorithms which solve the consensus and averaging problems on directed graphs with the least restrictive connectivity requirements. In this paper we study the convergence time of these algorithms. To this end, we investigate the shrinking time of the smallest interval that contains all states for the consensus algorithm, and the decay time of a suitable Lyapunov function for the averaging algorithm. The investigation leads us to characterize the convergence time by the hitting time in certain special Markov chains. We simplify the structures of state transition by considering the special case of complete graphs, where every edge can be activated with an equal probability, and derive polynomial upper bounds on convergence time.