On the Approximation Ratio of the MST-Based Heuristic for the Energy-Efficient Broadcast Problem in Static Ad-Hoc Radio Networks

We present a technique to evaluate the approximation ratio on random instances of the Minimum Energy Broadcast Problem in Ad-Hoc Radio Networks which is known to be NP-hard and approximable within 12. Our technique relies on polynomial-time computable lower bound on the optimal cost of any instance. The main result of this paper is that the approximation ratio has never achieved a value greater than 6.4. Furthermore, the worst values of this ratio are achieved for small network sizes. We also provide a clear geometrical motivation of such good approximation results.