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 (i.e., the overlapping of signals at network nodes) has certainly a positive effect, because it induces a reduction of the number of conflicting transmissions, and then results in an overall saving of energy consumption. Along this direction, in this paper we study the computational hardness of several interference minimization problems which arise while supporting some classic network communication patterns such as broadcasting (one-to-all), gossiping (all-to-all), and symmetric gossiping (symmetric all-to-all). In particular, concerning the non-approximability results, we prove that for any of the above communication patterns, the prominent problem 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. On a positive side, we show that any approximation algorithm for the problem of minimizing the total transmission power assigned to the nodes in order to guarantee any of the above communication patterns, can be transformed, by maintaining the same performance ratio, into an approximation algorithm for the problem of minimizing the total interference experienced by all the nodes in the network.