Distributed wireless link scheduling in the SINR model

We present an approximation algorithm for wireless link scheduling under the physical SINR interference model. In the link scheduling problem, it is given a set of \(n\) links in a metric space, each of which is a sender–receiver pair, and the objective is to schedule the links using the minimum amount of time. We focus on a variant of this fundamental problem where the power is fixed, i.e., the power assignment of links is given as part of the input. Specifically, we consider an important category of power assignments called length-monotone sublinear power assignment, which includes the widely studied uniform, mean and linear power assignments. We present a distributed algorithm that can schedule all links in \(O(\log \varDelta (I_{max}+\log ^3n))\) rounds with high probability, where \(\varDelta \) is the ratio between the longest link and the shortest link and \(I_{max}\) is the maximum nearly-equilength class affectance of the link set. It is shown that the proposed algorithm is \(O(\log \varDelta )\) approximate to the optimal schedule in dense networks with \(I_{max}\in \varOmega (\log ^3n)\). To the best of our knowledge, our algorithm is the first distributed one whose approximation ratio is independent of the network size \(n\). Our result also shows that the \(\varOmega (\log n)\) lower bound (Halldórsson and Mitra in: ICALP, 2011) on the approximation ratio does not hold for link sets with \(\log \varDelta \in o(\log n)\).