Wireless multi-rate scheduling: From physical interference to disk graphs

Wireless communication technology offers multi-rate transmission capability which allows to increase the network´s throughput. Nevertheless, previous algorithmic results have focused on single-rate radios. In this paper, we study the problem of scheduling multi-rate wireless requests considering the physical interference model. The objective of the problem is to select a subset of communication requests such that the sum of their data rates is maximized and no collisions occur if they are all scheduled simultaneously. We show that, under certain constraints on the input, the problem can be approximated by a graph-based model. More specifically, if network nodes live in a two-dimensional Euclidean space, where the path loss exponent is strictly larger than two, and if data rates and sender-receiver distances can only differ by a contact factor between communication requests, the problem can be modeled as a disk graph. This means that, despite the global nature of the physical interference model, conflicts between simultaneous requests can be restricted to the local neighborhood of the transmitting nodes. We show how to build the corresponding disk graph instances and prove that a weighted maximum independent set in this graph-based model provides a constant-factor approximation to the multi-rate scheduling problem in the physical interference model. Moreover, we implement a polynomial-time approximation scheme algorithm to obtain solutions that are within an arbitrarily small factor of being optimal in the disk graph model.