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

2025-12-24

AI Summary

Addressing the high computational cost of triplet counting and the lack of dynamic-update-friendly data structures in large-scale dynamic hypergraphs, this paper proposes ESCHER—a GPU-centric parallel hypergraph evolution representation. ESCHER is the first method to support unified, incremental maintenance of three types of triplets: hyperedge-based, vertex-association-based, and temporal. It integrates a dynamic indexing scheme, minimal-redundancy triplet enumeration, multi-granularity temporal evolution modeling, and pruning optimizations to enhance throughput. Evaluated on real-world and synthetic datasets, ESCHER achieves speedups of 104.5×, 473.7×, and 112.5× over state-of-the-art methods for hyperedge-, vertex-association-, and temporal-triplet updates, respectively. These improvements significantly advance real-time analysis of higher-order group interactions in dynamic hypergraphs.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Efficiently managing large dynamic hypergraph evolution
• Minimizing redundant computation in hypergraph triad counting
• Outperforming existing methods in hypergraph triad analysis

Innovation

• GPU-centric parallel data structure for hypergraph dynamics
• Hypergraph triad-count update framework minimizing redundant computation
• Validated across multiple triad types with significant speedups