Preliminary theoretical analysis of a local search algorithm to optimize network communication subject to preserving the total number of links

Abstract

A variety of phenomena such as world wide web, social or business interactions are modeled by various kinds of networks (such as the scale free or preferential attachment networks). However, due to the model-specific requirements one may want to rewire the network to optimize the communication among the various nodes while not overloading the number of channels (i.e. preserving the number edges). In the current paper we present a formal framework for this problem and a simple heuristic local search algorithm to cope with it. We estimate the expected single-step improvement of our algorithm, establish the ergodicity of the algorithm (i.e. that the algorithm never gets stuck at a local optima) with probability 1) and we also present a few initial empirical results for the scale free networks.