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.

中文翻译：

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无线网络调度的消息传递算法。

我们考虑在无线网络中进行调度，并将其表述为“冲突”图上的最大加权独立集（MWIS）问题，该图捕获了同时传输之间的干扰。我们提出了一种新颖的，低复杂度的，完全分布式的算法，可以产生高质量的可行解决方案。我们提出的算法包括两个阶段，每个阶段仅需要本地信息并且基于消息传递。第一阶段使用梯度投影方法解决了MWIS问题的松弛问题。我们考虑的松弛比简单的线性编程松弛更紧密，并且在图形中的所有类别上都包含了约束。该算法的第二阶段从松弛的解开始，为MWIS问题构建了可行的解。我们证明了我们的算法始终为完美图形提供针对MWIS问题的最佳解决方案。仿真结果将我们的策略与载波侦听多路访问（CSMA）和其他替代方案进行了比较，并显示了出色的性能。