Convergence Speed in Distributed Consensus and Averaging

Authors:
  • AOAlex Olshevsky
    Alex Olshevsky
  • JTJohn N. Tsitsiklis
    John N. Tsitsiklis
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Abstract
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.

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