A Message-Passing Algorithm for Wireless Network Scheduling.

We consider scheduling in wireless networks and formulate it as Maximum Weighted Independent Set (MWIS) problem on a "conflict" graph that captures interference among simultaneous transmissions. We propose a novel, low-complexity, and fully distributed algorithm that yields high-quality feasible solutions. Our proposed algorithm consists of two phases, each of which requires only local information and is based on message-passing. The first phase solves a relaxation of the MWIS problem using a gradient projection method. The relaxation we consider is tighter than the simple linear programming relaxation and incorporates constraints on all cliques in the graph. The second phase of the algorithm starts from the solution of the relaxation and constructs a feasible solution to the MWIS problem. We show that our algorithm always outputs an optimal solution to the MWIS problem for perfect graphs. Simulation results compare our policies against Carrier Sense Multiple Access (CSMA) and other alternatives and show excellent performance.