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.
Olshevsky and Tsitsiklis REF provided lower bounds on the worst-case convergence time for many different types of linear, time-invariant, distributed consensus algorithms.
Convergence speed in distributed consensus and averaging
IN PROC. OF THE 45TH IEEE CDC
Mathematics Computer Science