In the last decade, subgraph detection and enumeration have emerged as a central problem in distributed graph algorithms. This is largely due to the theoretical challenges and practical applications of these problems. 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 enumeration in our computational models and prove their optimality in two such models, (3)~introduce classes of sparse and ``everywhere sparse'' hypergraphs and describe efficient distributed algorithms for triangle 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：在过去的十年中，子图检测与枚举已成为分布式图算法中的一个核心问题。这主要源于这些问题的理论挑战与实际应用。在本文中，我们首次系统性地研究了超图中分布式子超图枚举问题。为此，我们（1）引入了若干种超图计算模型，这些模型推广了图的CONGEST模型，并评估了它们的相对计算能力；（2）在我们的计算模型中设计了分布式三角形枚举算法，并在其中两个模型中证明了其最优性；（3）引入了稀疏与“处处稀疏”的超图类，并描述了在这些类中高效的分布式三角形枚举算法；（4）描述了我们认为对设计超图模型中高效算法有用的一般性技术。