%0 Journal Article
%T Convergence Speed in Distributed Consensus and Control
%A Alex Olshevsky
%A John N. Tsitsiklis
%J Mathematics
%D 2006
%I arXiv
%X We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worst-case convergence time for various classes of linear, time-invariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a time-varying topology, and provide a polynomial-time averaging algorithm.
%U http://arxiv.org/abs/math/0612682v2