Simple, Fast, and Scalable Reachability Oracle

TL;DR

This paper introduces two new reachability oracle algorithms that are simple, fast, and scalable, significantly improving construction time and efficiency on large real-world graphs without needing transitive closure materialization.

Contribution

The paper presents Hierarchical-Labeling and Distribution-Labeling algorithms that outperform existing methods in speed and scalability for large graph reachability queries.

Findings

Construction time is an order of magnitude faster.

Index sizes and query performance surpass state-of-the-art methods.

No transitive closure materialization needed.

Abstract

A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) \cap Lin(v) \neq \emptyset. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: the main problem is high construction cost, which stems from a set-cover framework and the need to materialize transitive closure. In this paper, we present two simple and efficient labeling algorithms, Hierarchical-Labeling and Distribution-Labeling, which can work onmassive real-world graphs: their construction time is an order of magnitude faster than the setcover based labeling approach, and transitive closure materialization is not needed. On large graphs, their index sizes and their query performance can now beat the state-of-the-art transitive closure compression and online search approaches.