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Abstract

A scheme for consensus formation is considered wherein the value of a certain variable associated with the nodes of a network is fixed a priori for a prescribed set of K nodes, and allowed to propagate throughout the network through an averaging process that mimics a gossip algorithm. The objective is to find the best choice of these K nodes that will achieve the fastest convergence to consensus. This objective is captured by the Perron-Frobenius eigenvalue of the resultant sub-stochastic matrix, which then is the quantity one seeks to minimize. We propose an algorithm for this optimization problem, as well as a greedy scheme with some performance guarantees for a variant of the problem that seeks to minimize a simpler objective. Some other related formulations are also considered. ©2010 IEEE.