Optimal solutions for fault-tolerant topology control in wireless ad hoc networks

Topology control is one of the most important techniques used in wireless ad hoc and sensor networks to reduce energy consumption. Algorithms for topology control attempt to reduce the number of links and the power consumption in a network subject to connectivity constraints. We show that the related optimization problems may be classified into four main variants, regarding the topology of the input graph (symmetric or asymmetric) and of the solution (unidirectional or bidirectional). We present three mixed integer programming formulations for the k-connected minimum power consumption problem, which consists in finding a power assignment to the nodes of a wireless network so as that the resulting network topology be k-vertex connected (i.e., k-fault tolerant) and the total power consumption be minimum. These formulations are sufficiently general to encompass all four problem variants. We report computational experiments comparing the formulations. Optimal solutions for moderately sized networks are obtained using a commercial solver.