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.

翻译：超越成对关系的高阶交互在大规模复杂网络中通常被建模为超图。分析超图属性（如三元组计数）至关重要，因为超图能够揭示传统图无法捕获的复杂群体交互模式。在现实场景中，这些网络通常规模庞大且动态变化，带来了显著的计算挑战。由于缺乏专门的软件包和数据结构，大规模动态超图的分析仍未被充分探索。针对这一空白，我们提出ESCHER，一种面向GPU的并行数据结构，用于实现高效可扩展的超图演化表示，旨在高效管理大规模超图动态特性。我们还设计了一种超图三元组计数更新框架，能够在充分利用ESCHER动态操作能力的同时最小化冗余计算。我们针对多类超图三元组计数（包括超边基、关联顶点基和时间三元组）验证了方法的有效性。在大型真实与合成数据集上的实验结果表明，所提方法在超边基、关联顶点基和时间三元组类型上分别实现了高达104.5倍、473.7倍和112.5倍的加速，优于现有最优方法。