Topology Control Problems under Symmetric and Asymmetric Power Thresholds

We consider topology control problems where the goal is to assign transmission powers to the nodes of an ad hoc network so as to induce graphs satisfying specific properties. The properties considered are connectivity, bounded diameter and minimum node degree. The optimization objective is to minimize the total power assigned to nodes. As these problems are NP-hard in general, our focus is on developing approximation algorithms with provable performance guarantees. We present results under both symmetric and asymmetric power threshold models.