arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2107.03083cs.ITmath.IT
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具有离散传播延迟的无线网络调度:定理与算法

Wireless Network Scheduling with Discrete Propagation Delays: Theorems and Algorithms

Shenghao Yang, Jun Ma, Yanxiao Liu

AI总结:

针对离散传播延迟无线网络的链路调度问题,本文用有向超图建模并提出调度图表征速率区域,进一步利用 step-T 调度图的支配性质设计更高效算法。

摘要:

本文聚焦于节点间信号延迟为某个时间间隔整数倍的网络中的链路调度问题。为对此类网络建模,采用了有向超图以及一个指定延迟的整数矩阵。链路调度问题与由网络模型导出的周期超图的独立集密切相关。然而,由于顶点数量无限,使用通用图算法枚举周期超图的独立集是不切实际的。为应对这一挑战,本文提出了一种图论方法。利用一个由网络模型导出、称为调度图的有限有向图来刻画链路调度速率区域。网络的无冲突调度对应于调度图中的一条路径,而速率区域由调度图中各环相关联的速率向量的凸包决定。尽管现有环枚举算法可用于计算速率区域,但随着调度图规模随网络链路数量呈指数增长,其计算复杂度会高得令人难以承受。为解决该问题,研究了一种称为 step-T 调度图的特殊调度图的支配性质。该性质允许利用 step-T 调度图的特定子图来刻画调度速率区域,从而同时减少环的数量及其长度。针对计算速率区域以及最大化调度速率加权和等常见问题,开发了利用该支配性质的算法。与直接在调度图上使用通用图算法相比,这些算法可能更高效。

英文摘要:

This paper focuses on the link scheduling problem in networks where signal delays between nodes are multiples of a time interval. To model such networks, a directed hypergraph is employed, along with an integer matrix that specifies the delays. The link scheduling problem is closely connected to the independent sets of the periodic hypergraph induced by the network model. However, due to the infinite number of vertices, it is impractical to enumerate the independent sets of the periodic hypergraph using generic graph algorithms. To tackle this challenge, a graphical approach is proposed in this paper. The link scheduling rate region is characterized using a finite directed graph called a scheduling graph, which is derived from the network model. A collision-free schedule of the network corresponds to a path in the scheduling graph, and the rate region is determined by the convex hull of the rate vectors associated with the cycles in the scheduling graph. Although existing cycle enumeration algorithms can be employed to calculate the rate region, their computational complexity becomes prohibitively high as the size of the scheduling graph grows exponentially with the number of network links. To address this issue, the dominance property of a special scheduling graph called the step-T scheduling graph is investigated. This property allows the utilization of specific subgraphs of the step-T scheduling graph to characterize the scheduling rate region, achieving a reduction in both the number of cycles and their lengths. For common problems such as calculating the rate region and maximizing a weighted sum of the scheduling rates, algorithms leveraging the dominance property are developed. These algorithms can be more efficient than using generic graph algorithms directly on the scheduling graphs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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