可扩展的近似算法：面向动态最密子超图的问题引导维护
Scalable Approximate Algorithm for Dynamic Densest Subhypergraphs with Solution-Guided Maintenance
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- CUHK-Shenzhen（香港中文大学（深圳））
- SLAI（深圳高等研究院）
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中文总结 AI 辅助
提出CAP算法，通过候选解密度引导维护，在超边动态增删下高效维护$(1+\epsilon)$-近似最密子超图，实验显示比动态基线快近四个数量级。
中文摘要 AI 辅助
超图建模了涉及实体组之间的交互，而寻找高度连接的组是分析这些数据的基本任务。当交互到达和过期时，维护一个密集的组可能需要对底层表示进行频繁且昂贵的更改。我们提出了CAP，一种可扩展的算法，它在超边插入和删除下显式维护一个$(1+\epsilon)$-近似的最大密度子超图。该算法保持一个候选解以及一个端点分配，该分配界定了最优密度。候选解的密度引导维护：仅当该界限过大而无法建立所需的近似时，更新才触发修复。局部搜索重新分配负载或寻找更密集的候选解，使CAP能够在多次更新中保留有用的解。我们给出了一种分析，将维护工作与搜索区域的大小以及维护解所损失的密度联系起来。它确定了局部修复保持廉价的条件，并为观察到的效率提供了理论解释。在真实世界超图上的实验显示，与评估的动态基线相比，加速比高达近四个数量级，同时支持频繁查询和高准确性。CAP在普通图上与专门的动态图方法相比也保持竞争力，在测试的工作负载上加速比高达约$64\times$。
英文摘要
Hypergraphs model interactions involving groups of entities, and finding highly connected groups is a fundamental task in analyzing these data. When interactions arrive and expire, maintaining a dense group can require frequent and expensive changes to the underlying representation. We propose CAP, a scalable algorithm that explicitly maintains a $(1+ε)$-approximate densest subhypergraph under hyperedge insertions and deletions. The algorithm keeps a solution candidate together with an endpoint allocation that bounds the optimum density. The candidate's density guides maintenance: an update triggers repair only when this bound is too large to establish the required approximation. Local searches redistribute load or find a denser candidate, allowing CAP to retain useful solutions across many updates. We give an analysis that relates maintenance work to the size of the regions searched and the density lost by the maintained solution. It identifies conditions under which local repair remains inexpensive and provides a theoretical explanation for the observed efficiency. Experiments on real-world hypergraphs show speedups of up to nearly four orders of magnitude over the evaluated dynamic baselines, while supporting frequent queries and high accuracy. CAP also remains competitive with specialized dynamic graph methods on ordinary graphs, with speedups of up to approximately $64\times$ on the tested workloads.
