Power optimization in ad hoc wireless network topology control with biconnectivity requirements

We consider the problem of assigning transmission powers to the nodes of an ad hoc wireless network, so that the total power consumed is minimized and the resulting network is biconnected, i.e., there are at least two node-disjoint paths between any pair of nodes. Biconnected communication graphs are important to ensure fault tolerance, since ad hoc networks are used in critical application domains where failures are likely to occur. A mixed integer programming formulation of the problem can be exactly solved to optimality by a commercial solver only for moderately sized problems. We recall a mixed integer programming formulation that can be exactly solved to optimality by a commercial solver only for very moderately sized problems. We propose a quick greedy algorithm and a GRASP with path-relinking heuristic for solving real-life sized problems. Computational experiments involving practical issues such as energy consumption and interference have been performed and reported for problems with up to 800 nodes, illustrating the effectiveness and the efficiency of the new algorithms. Both the greedy algorithm and the GRASP heuristic outperformed the best heuristic in the literature for very large problem sizes.