In the last decade, subgraph detection and enumeration have emerged as central problems in distributed graph algorithms. This is largely due to the problems' theoretical challenges and practical applications. In this paper, we initiate the systematic study of distributed sub-hypergraph enumeration in hypergraphs. To this end, we (1) introduce several computational models for hypergraphs that generalize the CONGEST model for graphs and evaluate their relative computational power, (2) devise algorithms for distributed triangle and simplex enumeration in our computational models and prove their optimality in two such models by showing matching lower bounds, (3) introduce classes of sparse and "everywhere sparse" hypergraphs and describe efficient distributed algorithms for triangle and simplex enumeration in these classes, and (4) describe general techniques that we believe to be useful for designing efficient algorithms in our hypergraph models.

翻译：在过去十年中，子图检测与枚举已成为分布式图算法中的核心问题，这主要源于其理论挑战性和实际应用价值。本文首次系统研究了超图中的分布式子超图枚举问题。为此，我们：(1) 提出若干基于图的CONGEST模型泛化的超图计算模型，并评估其相对计算能力；(2) 在这些计算模型中设计分布式三角形和单纯形枚举算法，并通过匹配下界证明其在两个模型中的最优性；(3) 引入稀疏超图和“处处稀疏”超图等类别，描述其中高效的分布式三角形和单纯形枚举算法；(4) 提出我们认为对在超图模型中设计高效算法具有普适性的通用技术。