An assumption that has often been used by researchers to model the 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 values of the path loss exponent of signal propagation. We also investigate hypergraphs generated by line networks.

翻译：研究者们常用单位圆盘图模型来建模无线网络中的干扰。尽管在该模型下已获得诸多理论结果和性能保证，但将这些结果拓展至超图干扰模型仍是一个开放的研究方向。受近期关于分布式最大调度算法在最坏情况下的性能由超图干扰度刻画这一结果的启发，本研究探讨了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，并推导了关于该超图不变量的若干性质与结论。我们研究了哪些超图是可实现的，即基于物理约束，哪些超图在实际中可作为无线网络的干扰模型。特别地，一个自然产生的问题是：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不同取值确定了该值，并进一步研究了由线形网络生成的超图。