On the approximability of the range assignment problem on radio networks in presence of selfish agents

We consider the range assignment problem in ad-hoc wireless networks in the context of selfish agents: A network manager aims to assigning transmission ranges to the stations in order to achieve strong connectivity of the network within a minimal overall power consumption. Station is not directly controlled by the manager and may refuse to transmit with a certain transmission range because it might be costly in terms of power consumption. We investigate the existence of payment schemes which induce the stations to follow the decisions of a network manager in computing a range assignment, that is, truthful mechanisms for the range assignment problem. We provide both positive and negative results on the existence of truthful VCG-based mechanisms for this NP-hard problem. We prove that (i) in general, every polynomial-time truthful VCG-based mechanism computes a solution of cost far-off the optimum, unless P=NP and (ii) there exists a polynomial-time truthful VCG-based mechanism achieving constant approximation for practically relevant, still NP-hard versions, i.e., the metric and the well-spread case.