In this article, we address the scheduling problem in wireless ad hoc networks by exploiting the computational advantage that comes when scheduling problems can be represented by claw-free conflict graphs where we consider a wireless broadcast medium. It is possible to formulate a scheduling problem of broadcast transmissions as finding the maximum weighted independent set (MWIS) in the conflict graph of the network. Finding the MWIS of a general graph is NP-hard leading to an NP-hard complexity of scheduling. In a claw-free conflict graph, MWIS may be found in polynomial time leading to a throughput-optimal scheduling. We show that the conflict graphs of certain wireless ad hoc networks are claw-free. In order to obtain claw-free conflict graphs in general networks, we suggest introducing additional conflicts (edges) with the aim of keeping the decrease in MWIS size minimal. To this end, we introduce an iterative optimization problem to decide where to introduce edges and investigate its efficient implementation. We conclude that the claw breaking method by adding extra edges can perform very close to optimal scenario and better than the polynomial time maximal independent set scheduling benchmark under the necessary assumptions.

中文翻译：

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一种多项式时间无线自组网调度的新方法

在本文中，我们通过利用计算优势来解决无线自组织网络中的调度问题，当调度问题可以用无爪冲突图表示时，我们考虑无线广播介质。可以将广播传输的调度问题表述为在网络冲突图中寻找最大加权独立集 (MWIS)。找到一般图的 MWIS 是 NP-hard 导致调度的 NP-hard 复杂性。在无爪冲突图中，可以在多项式时间内找到 MWIS，从而实现吞吐量优化调度。我们表明某些无线自组织网络的冲突图是无爪的。为了获得一般网络中的无爪冲突图，我们建议引入额外的冲突（边缘），以保持 MWIS 大小的减少最小。为此，我们引入了一个迭代优化问题来决定在何处引入边并研究其有效实现。我们得出的结论是，在必要的假设下，通过添加额外边的爪破方法可以非常接近最佳场景，并且优于多项式时间最大独立集调度基准。