There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm $\mathcal{A}$ for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm $\mathcal{A}$, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a constant.

中文翻译：

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对给定度数的超图进行采样

超图和二部图之间有一个众所周知的联系，通过将超图的关联矩阵视为二部图的双邻接矩阵而获得。我们使用这种连接来描述和分析一种拒绝采样算法，用于对具有给定度数序列的简单均匀超图进行采样。我们的算法使用作为黑盒的算法 $\mathcal{A}$ 在（预期的）多项式时间内均匀或几乎均匀地对具有给定度数的二部图进行采样。超图采样算法的预期运行时间取决于二部图采样算法 $\mathcal{A}$ 的（预期）运行时间，以及具有给定度数的均匀随机二部图对应于简单超图的概率。