Power efficient range assignment in ad-hoc wireless networks

We study the problem of assigning transmission ranges to the nodes of ad hoc wireless networks to minimize power consumption while ensuring network connectivity. We give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 35-40 nodes in 1 hour; a proof that min-power symmetric connectivity with asymmetric power requirements is inapproximable within factor (1 - ε) ln |V| for any ε > 0 unless P = NP; an improved analysis for two approximation algorithms recently proposed by Calinescu et al. (TCS´02), decreasing the best known approximation factor to 5/3 + ε; and a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.