论文标题
在蜂窝移动通信系统中产生的超图的结构
The Structure of Hypergraphs Arising in Cellular Mobile Communication Systems
论文作者
论文摘要
单位磁盘图模型是研究人员经常用来模拟无线网络中干扰的假设。尽管在此模型下获得了许多理论结果和性能保证，但开放的研究方向是将这些结果扩展到HyperGraph Interperience模型。最近的结果是，分布式最大调度算法的最差案例性能的特征是超毛图的干扰程度，在当前的工作中，我们研究了超图的干扰程度和由物理约束产生的超毛孔结构的特性。我们表明，计算超图的干扰程度的问题是NP- hard，我们证明了有关此超图形不变的一些属性和结果。我们研究了哪些超图可实现，即基于物理约束作为无线网络的干扰模型，在实践中出现了哪些超图。特别是，一个自然出现的问题是：$ r $的最大值是什么，使得hypergraph $ k_ {1，r} $可实现？我们确定了信号传播路径损失指数的各种积分和非整合值的数量。我们还研究了线网络生成的超图。
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.
