Exploiting Geometry in the SINR\(_k\) Model

We introduce the SINR\(_k\) model, which is a practical version of the SINR model. In the SINR\(_k\) model, in order to determine whether \(s\)’s signal is received at \(c\), where \(s\) is a sender and \(c\) is a receiver, one only considers the \(k\) most significant senders w.r.t. to \(c\) (other than \(s\)). Assuming uniform power, these are the \(k\) closest senders to \(c\) (other than \(s\)). Under this model, we consider the well-studied scheduling problem: Given a set \(L\) of sender-receiver requests, find a partition of \(L\) into a minimum number of subsets (rounds), such that in each subset all requests can be satisfied simultaneously. We present an \(O(1)\)-approximation algorithm for the scheduling problem (under the SINR\(_k\) model). For comparison, the best known approximation ratio under the SINR model is \(O(\log n)\). We also present an \(O(1)\)-approximation algorithm for the maximum capacity problem (i.e., for the single round problem), obtaining a constant of approximation which is considerably better than those obtained under the SINR model. Finally, for the special case where \(k=1\), we present a PTAS for the maximum capacity problem. Our algorithms are based on geometric analysis of the SINR\(_k\) model.