  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.
