Some Valid Inequalities for the Probabilistic Minimum Power Multicasting Problem

In this paper we describe some results on the linear integer programming formulation of the Probabilistic Minimum Power Multicast (PMPM) problem for wireless networks. The PMPM problem consists in optimally assigning transmission powers to the nodes of a given network in order to establish a multihop connection between a source node and a set of destination nodes. The nodes are subject to failure with some probability, however the assignment should be made so that the reliability of the connection is above a given threshold level. This model reflects the necessity of taking into account the uncertainty of hosts’ availability in a telecommunication network.