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 integral and nonintegral values of the path loss exponent of signal propagation. We also investigate hypergraphs generated by line networks.

翻译：研究者常采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许多理论结果和性能保证，但将这些结果推广至超图干扰模型仍是一个开放的研究方向。受最新研究成果（分布式最大调度算法的最差情况性能由超图的干扰度表征）的启发，本文研究了超图干扰度的性质及其物理约束下生成的超图结构。我们证明计算超图干扰度是NP困难问题，并推导出与该超图不变量相关的若干性质与结论。进一步探究哪些超图是可实现的——即基于物理约束，哪些超图可在实际无线网络干扰模型中生成。特别地，一个自然产生的问题是：使得超图$K_{1,r}$可实现的参数$r$的最大值是多少？我们针对信号传播路径损耗指数的整数与非整数值分别确定了该量值，并研究了由线性网络生成的超图。