Minimum power multicasting in wireless networks under probabilistic node failures

In this paper we deal with a new probabilistic extension of the Minimum Power Multicast (MPM) problem for wireless networks. The deterministic MPM problem consists in assigning transmission powers to the nodes, so that a multihop connection can be established between a source and a given set of destination nodes and the total power required is minimized. We present a new extension to the basic problem, where node failure probabilities for the transmission are explicitly considered. This model reflects the necessity of taking uncertainty into account in the availability of the hosts. The novelty of the Probabilistic Minimum Power Multicast (PMPM) problem treated in this paper consists in the minimization of the assigned transmission powers, imposing at the same time a global reliability level to the solution network. An integer linear programming formulation for the PMPM problem is presented. Furthermore, an exact algorithm based on an iterative row and column generation procedure, as well as an heuristic method are proposed. Computational experiments are finally presented. keywords: Minimum Power Multicasting, Probabilistic Mathematical Models, Multihop Networks.