A Graph-Based Algorithm for Scheduling with Sum-Interference in Wireless Networks

For decades, a disk-graph model has been used to design scheduling (coloring) in wireless networks, influencing many practical medium access control schemes. The pairwise - interference model used by a disk graph, however, has a fundamental limitation because it does not account for the sum- interference. Thus, a coloring algorithm that uses such a model cannot guarantee the originally intended rate on all links. In this paper, we specify a mapping to a flow-contention graph, which fully considers the aggregated effect of all interferers (sum- interference), and thus, guarantees the originally intended rate on all links. A coloring algorithm, specific to the generated graph, is presented along with a bound on the required number of colors (channels). Further, a mathematical analysis of the scheduling is presented along with simulation results, to show that the minimum number of channels required in a random network is Theta(logn/log log n), where n is the number of links, even after accounting for the sum-interference. This allows us to investigate the effect of the underlying physical layer, thus demonstrating the utility of the presented algorithm and analysis results.