HL-index: Fast Reachability Query in Hypergraphs

2025-12-29

AI Summary

This paper investigates the maximum *s*-reachability query problem on hypergraphs: given a source and a target vertex, determine the largest *s* such that there exists a sequence of hyperedges where each pair of consecutive hyperedges intersects in at least *s* vertices, and the source and target belong to the first and last hyperedges, respectively. We formally define *s*-reachability and max-reachability for the first time. To address this problem efficiently, we propose a lightweight HL-index (mapping vertices to incident hyperedges) and a neighbor-relation caching mechanism, integrated with fast coverage-relation checking and traversal pruning strategies. These techniques jointly reduce both indexing overhead and query latency. Extensive evaluation on 20 real-world and synthetic datasets demonstrates that our approach accelerates queries by one to two orders of magnitude over baseline methods, while yielding compact indexes with rapid construction time and excellent scalability.

Technology Category

• Search and Optimization: Heuristic Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web crawling and indexing
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

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.

Problem

• Develop HL-index for max-reachability queries in hypergraphs
• Generalize s-reachability to model complex groupwise interactions
• Overcome limitations of existing indexing techniques for hypergraphs

Innovation

• Introduces HL-index for hypergraph reachability queries
• Develops fast covering detection to minimize index construction
• Uses lightweight neighbor-index to accelerate relationship exploration