ESCHER: Efficient and Scalable Hypergraph Evolution Representation with Application to Triad Counting

TL;DR

ESCHER introduces a GPU-based data structure and framework for efficient, scalable analysis of large, dynamic hypergraphs, significantly accelerating triad counting tasks in complex network analysis.

Contribution

The paper presents ESCHER, a novel GPU-centric data structure and update framework for hypergraph evolution, enabling fast analysis of large, dynamic hypergraphs.

Findings

Achieves up to 104.5x speedup in hyperedge triad counting

Achieves up to 473.7x speedup in incident-vertex triad counting

Achieves up to 112.5x speedup in temporal triad counting

Abstract

Higher-order interactions beyond pairwise relationships in large complex networks are often modeled as hypergraphs. Analyzing hypergraph properties such as triad counts is essential, as hypergraphs can reveal intricate group interaction patterns that conventional graphs fail to capture. In real-world scenarios, these networks are often large and dynamic, introducing significant computational challenges. Due to the absence of specialized software packages and data structures, the analysis of large dynamic hypergraphs remains largely unexplored. Motivated by this gap, we propose ESCHER, a GPU-centric parallel data structure for Efficient and Scalable Hypergraph Evolution Representation, designed to manage large scale hypergraph dynamics efficiently. We also design a hypergraph triad-count update framework that minimizes redundant computation while fully leveraging the capabilities of ESCHER for dynamic operations. We validate the efficacy of our approach across multiple categories of hypergraph triad counting, including hyperedge-based, incident-vertex-based, and temporal triads. Empirical results on both large real-world and synthetic datasets demonstrate that our proposed method outperforms existing state-of-the-art methods, achieving speedups of up to 104.5x, 473.7x, and 112.5x for hyperedge-based, incident-vertex-based, and temporal triad types, respectively.