arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2207.00515cs.NIcs.CCcs.DMcs.DS
收藏

蜂窝移动通信系统中出现的超图结构

The Structure of Hypergraphs Arising in Cellular Mobile Communication Systems

Ashwin Ganesan

AI总结:

本文研究蜂窝移动通信中由物理约束产生的超图干扰模型,证明干扰度计算 NP 难,并确定不同路径损耗指数下 K_{1,r} 的最大可实现 r。

摘要:

研究人员在无线网络中对干扰进行建模时经常采用的一个假设是单位圆盘图模型。尽管在该模型下已经获得了许多理论结果和性能保证,但一个开放的研究方向是将这些结果扩展到超图干扰模型。受近期结果的启发,即分布式最大调度算法的最坏情况性能由超图的干扰度刻画,在本工作中,我们研究超图干扰度的性质以及由物理约束产生的超图结构。我们证明计算超图干扰度的问题是 NP 难的,并证明了关于该超图不变量的一些性质和结果。我们研究哪些超图是可实现的,即在实际中基于物理约束,哪些超图会作为无线网络的干扰模型出现。特别地,一个自然出现的问题是:使超图 K_{1,r} 可实现的 r 的最大值是多少?我们针对信号传播路径损耗指数的各种整数和非整数值确定了这一量。我们还研究了由线性网络生成的超图。

英文摘要:

An assumption that researchers have often used to model interference in a wireless network is the unit disk graph model. While many theoretical results and performance guarantees have been obtained under this model, an open research direction is to extend these results to hypergraph interference models. Motivated by recent results that the worst-case performance of the distributed maximal scheduling algorithm is characterized by the interference degree of the hypergraph, in the present work we investigate properties of the interference degree of the hypergraph and the structure of hypergraphs arising from physical constraints. We show that the problem of computing the interference degree of a hypergraph is NP-hard and we prove some properties and results concerning this hypergraph invariant. We investigate which hypergraphs are realizable, i.e. which hypergraphs arise in practice, based on physical constraints, as the interference model of a wireless network. In particular, a question that arises naturally is: what is the maximal value of $r$ such that the hypergraph $K_{1,r}$ is realizable? We determine this quantity for various integral and nonintegral values of the path loss exponent of signal propagation. We also investigate hypergraphs generated by line networks.

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。

↑