论文标题
给定度的抽样超图
Sampling hypergraphs with given degrees
论文作者
论文摘要
通过将HyperGraph的入射矩阵视为双分部分图的双jaCencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencencency矩阵，可以获得众所周知的连接。我们使用此连接来描述和分析具有给定度序列的简单均匀超图的拒绝采样算法。我们的算法用作黑匣子，是一个算法$ \ Mathcal {a} $，用于在（预期的）多项式时间中均匀或几乎均匀地采样具有给定学位的两部分图。 HyperGraph采样算法的预期运行时间取决于双分组图采样算法的（预期）运行时（预期的）运行时$ \ MATHCAL {A a} $，以及具有给定度相对应的均匀随机的两部分图形的概率。我们给出了超图学序列的某些条件，这些条件确保该概率在下面以正常数为界。
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 positive constant.
