Distributed Triangle Enumeration in Hypergraphs

2026-02-19

AI Summary

This work addresses the challenge that traditional graph models struggle to capture higher-order relationships by presenting the first systematic study of distributed triangle enumeration on hypergraphs. We propose a hypergraph communication framework based on a generalized CONGEST model, introduce the notions of sparse and globally sparse hypergraphs, and develop general techniques for designing distributed algorithms in this setting. Building upon this foundation, we devise triangle enumeration algorithms that achieve optimal or near-optimal communication complexity across multiple hypergraph computation models. Notably, our algorithms significantly outperform existing approaches in sparse hypergraph scenarios, demonstrating both theoretical efficiency and practical relevance for higher-order network analysis.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• distributed triangle enumeration
• hypergraphs
• sub-hypergraph enumeration
• distributed algorithms

Innovation

• distributed algorithms
• hypergraphs
• triangle enumeration
• CONGEST model
• sparse hypergraphs