The “Real” Approximation factor of the MST heuristic for the Minimum Energy Broadcasting

The paper deals with one of the most studied problems during the last years in the field of wireless communications in Ad-Hoc networks. The problem consists in reducing the total energy consumption of wireless radio stations randomly spread on a given area of interest to perform the basic pattern of communication given by the Broadcast. Recently an almost tight 6.33-approximation of the Minimum Spanning Tree heuristic has been proved [8]. While such a bound is theoretically close to optimum compared to the known lower bound of 6 [10], there is an evident gap with practical experimental results. By extensive experiments, proposing a new technique to generate input instances and supported by theoretical results, we show how the approximation ratio can be actually considered close to 4 for a “real world” set of instances, that is, instances with a number of nodes more representative of practical purposes.