A Lower Bound for Distributed Averaging Algorithms on the Line Graph
Alex Olshevsky, John N. Tsitsiklis · IEEE Transactions on Automatic Control · 2011
We derive lower bounds on the convergence speed of a widely used class of distributed averaging algorithms. In particular, we prove that any distributed averaging algorithm whose state consists of a single real number and whose (possibly nonlinear) update function satisfies a natural smoothness condition has a worst case running time of at least on the order ofn2on a line network ofnnodes. Our results suggest that increased memory or expansion of the state space is crucial for improving the running times of distributed averaging algorithms.