LP-relaxation based distributed algorithms for scheduling in wireless networks

LP relaxations of Maximum Weighted Independent Set (MWIS) problems have been widely studied. A key motivation for this prior work comes from the central role that MWIS plays in designing throughput-optimal algorithms for wireless networks. However, to the best of our knowledge, the actual packet delay performance of these algorithms has not been studied in the context of wireless networks. In this paper, we first present an algorithm for solving the LP relaxation of MWIS which exhibits faster convergence to an optimal solution. Further, we show that one does not have to wait for infinite time for convergence to occur, but a simple rounding technique can be used to identify the ON/OFF states of the wireless links in finite time. As in prior work, such an approach only identifies the optimal MWIS states of some of the links in the network. Therefore, we present a scheme to combine this solution with Q-CSMA. Simulations indicate that the proposed scheme significantly improves the performance of Q-CSMA. Further, the proposed algorithm is shown to perform much better than previously suggested LP relaxation schemes due to its superior convergence properties.