Distributed Triangle Enumeration in Hypergraphs

TL;DR

This paper explores distributed algorithms for triangle enumeration in hypergraphs, introducing new models, algorithms, and techniques to improve efficiency and optimality in sub-hypergraph detection.

Contribution

It introduces hypergraph computational models, develops optimal distributed triangle enumeration algorithms, and proposes techniques for efficient hypergraph processing.

Findings

Optimal algorithms for triangle enumeration in hypergraphs.

Efficient algorithms for sparse and everywhere sparse hypergraphs.

New computational models generalizing the CONGEST model.

Abstract

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.