On the complexity of minimizing interference in ad-hoc and sensor networks

One of the most critical factors for lifetime and operability of ad-hoc and sensor networks is the limited amount of available energy. To this respect, minimizing the interference in the network has certainly a positive effect, since of the reduced number of conflicting transmissions. However, quite surprisingly, only few theoretical results are known about the possibility to maintain the interference low while at the same time guaranteeing certain network connectivity properties. In this paper, we give a contribution in this direction, and we study several network interference measures with respect to the symmetric connectivity, the strong connectivity, and the broadcast connectivity predicate. In particular, we show that the probably most prominent interference problem, namely that of minimizing the maximum interference experienced by any node in the network, is hard to approximate within better than a logarithmic factor, unless NP admits slightly superpolynomial time algorithms, for any of the above connectivity predicates. On a positive side, we show that any approximation algorithm for the problem of minimizing the total range assigned to the nodes in order to guarantee any of the above connectivity predicates, can be transformed, by maintaining the approximation ratio, into an approximation algorithm for the problem of minimizing the total interference experienced by all the nodes in the network.