HL-index: Fast Reachability Query in Hypergraphs

TL;DR

This paper introduces the HL-index, a novel indexing method for fast max-reachability queries in hypergraphs, enabling efficient analysis of complex group interactions in various real-world applications.

Contribution

The paper presents the HL-index, a new compact index for max-reachability in hypergraphs, along with a fast construction method using relationship detection and neighbor-indexing.

Findings

HL-index significantly improves query efficiency.

The approach scales well to large datasets.

Experimental results validate the method's effectiveness.

Abstract

Reachability in hypergraphs is essential for modeling complex groupwise interactions in real-world applications such as co-authorship, social network, and biological analysis, where relationships go beyond pairwise interactions. In this paper, 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 hyperedges 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.