The feasibility of matchings in a wireless network

Scheduling is important in wireless networks for two reasons. First, a schedule of minimum length provides an upper bound on the network's throughput. Second, scheduling is necessary to avoid collisions. Collisions cost energy, making them undesirable in wireless networks whose nodes have limited energy. To produce good link schedules we need large activation sets, sets of links, which can be used concurrently. We call these "feasible matchings". The larger a matching, greater is the parallelism, and the shorter the schedule. In this work, we prove theorems that show how to infer whether certain sets of links are feasible or not, without actually computing eigenvalues.