Reachability in hypergraphs is essential for mod- eling complex groupwise interactions in real-world applications such as co-authorship, social network, and biological analysis, where relationships go beyond pairwise interactions. In this pa- per, we introduce the notion of s-reachability, where two vertices are s-reachable if there exists a sequence of hyperedges (i.e., a walk) connecting them, such that each pair of consecutive hy- peredges shares at least s vertices. Moreover, we define the max- reachability query as a generalized form of the s-reachability problem, which aims to find the largest value of s that allows one vertex to reach another. To answer max-reachability queries in hypergraphs, we first analyze limitations of the existing vertex-to- vertex and hyperedge-to-hyperedge indexing techniques. We then introduce the HL-index, a compact vertex-to-hyperedge index tailored for the max-reachability problem. To both efficiently and effectively construct a minimal HL-index, we develop a fast covering relationship detection method to eliminate fruitless hypergraph traversals during index construction. A lightweight neighbor-index is further proposed to avoid repeatedly exploring neighbor relationships in hypergraphs and hence accelerate the construction. Extensive experiments on 20 datasets demonstrate the efficiency and scalability of our approach.

翻译：超图中的可达性对于建模现实应用（如合著关系、社交网络和生物分析）中的复杂群体交互至关重要，这些场景中的关系超越了成对交互。本文引入了s-可达性概念：若两个顶点间存在由超边构成的序列（即游走）连接，且每对相邻超边至少共享s个顶点，则称这两个顶点是s-可达的。进一步地，我们将最大可达性查询定义为s-可达性问题的广义形式，其目标是寻找使一个顶点可达另一个顶点的最大s值。为回答超图中的最大可达性查询，我们首先分析了现有顶点-顶点与超边-超边索引技术的局限性，随后提出了HL-index——一种专为最大可达性问题设计的紧凑型顶点-超边索引。为高效构建最小化HL-index，我们开发了快速覆盖关系检测方法以消除索引构建过程中无效的超图遍历，并进一步提出轻量级邻居索引以避免重复探索超图中的邻接关系，从而加速构建过程。在20个数据集上的大量实验证明了我们方法的高效性与可扩展性。