Minimizing interference in ad-hoc networks with bounded communication radius

We consider a topology control problem in which we are given a set of $n$ sensors in the plane and we would like to assign a communication radius to each of them. The radii assignment must generate a strongly connected network and have low receiver-based interference (i.e., we minimize the largest in-degree of the network). We give an algorithm that generates a network with $O(\log \Delta)$ interference, where $\Delta$ is the interference of a uniform-radius ad-hoc network. We then adapt the construction to the case in which no sensor can have a communication radius larger than $R_{\min}$, the minimum value needed to obtain connectivity. We also show that $\log \Delta$ interference is needed for some instances, making our algorithms asymptotically optimal.