<i>OTM</i> : Efficient <i>k</i> -Order-Based Core Maintenance in Large-Scale Dynamic Hypergraphs

The k -core model has garnered widespread adoption for preserving essential cohesive subgraphs owing to its linear-time computability, making it particularly suitable for hypergraph analysis. However, considering the continuously evolving characteristics of real-world hypergraphs, recent research efforts have focused on developing efficient algorithms that can maintain the core value of each vertex amid structural alterations. Despite these efforts, frequent insertions and deletions in dynamic hypergraphs continue to pose significant inefficiencies, primarily due to the increased traversal overhead incurred by hyperedge insertion algorithms. This exacerbates performance disparities between handling hyperedge insertions and deletions, underscoring the persistent challenge of effective k -core analysis in hypergraphs. To effectively address these challenges, we have gained key insights that enable us to define a specific order, termed the hypergraph k -order, which significantly reduces redundant vertex traversal and narrows down the search space during hyperedge insertions. Based on the proposed hypergraph k -order, we define two indices, the order index and the pivotal index, aimed at minimizing traversal costs and expediting the hyperedge insertion algorithm. Moreover, it is essential to recognize that the recomputation of the support degree ( sd ) for all vertices following each hyperedge deletion can significantly diminish the performance efficiency of deletion algorithms. To address this, we introduce an optimized approach that leverages the incremental maintenance of the support degree ( sd ) value to expedite the hyperedge deletion process. By leveraging these optimizations, we introduce a novel Order-based Traversal core Maintenance methodology, designated as OTM , which markedly enhances the efficiency of core maintenance in dynamic hypergraphs. Our comprehensive evaluation, which covers 12 real-world hypergraph datasets and a synthetic dataset, reveals that OTM achieves staggering speedup, outperforming the state-of-the-art approach with a 41,420 \(\times\) speedup in the insertion algorithm and 8,284 \(\times\) speedup in the deletion algorithm, underscoring its remarkable efficiency and effectiveness.