Maximal Scheduling in a Hypergraph Model for Wireless Networks

We introduce a hypergraph based interference model for scheduling in wireless networks. As a generalization of the graph model, hypergraph considers the conflicts caused by sum interference. We show in an arbitrary network, the successful transmissions under any graph model can be improved by a hypergraph. In some networks, a hypergraph can double the uniform throughput compared to the disk graph. We then analyze the capacity region of maximal scheduling in the hypergraph, where a linear programming (LP) based lower bound is formulated and proven to be tight. We also show that the maximal scheduling in hypergraph can guarantee a certain fraction of the capacity region. Simulation results show that maximal scheduling in hypergraph can achieve about 40% more uniform throughput than in graph for random networks.