O'Reach: Even Faster Reachability in Large Graphs

TL;DR

This paper introduces O'Reach, a new linear-sized reachability index that enables constant-time queries in large directed graphs, significantly improving speed and efficiency over previous methods through innovative algorithmic combinations and extensive experiments.

Contribution

The paper presents O'Reach, a novel algorithm that supports fast reachability queries, can be integrated with existing solutions, and demonstrates superior performance in diverse graph scenarios.

Findings

O'Reach achieves constant-time reachability queries.

Combining O'Reach with existing algorithms accelerates performance.

Higher space investment does not always improve query speed due to cache effects.

Abstract

One of the most fundamental problems in computer science is the reachability problem: Given a directed graph and two vertices s and t, can s reach t via a path? We revisit existing techniques and combine them with new approaches to support a large portion of reachability queries in constant time using a linear-sized reachability index. Our new algorithm O'Reach can be easily combined with previously developed solutions for the problem or run standalone. In a detailed experimental study, we compare a variety of algorithms with respect to their index-building and query times as well as their memory footprint on a diverse set of instances. Our experiments indicate that the query performance often depends strongly not only on the type of graph, but also on the result, i.e., reachable or unreachable. Furthermore, we show that previous algorithms are significantly sped up when combined with our new approach in almost all scenarios. Surprisingly, due to cache effects, a higher investment in space doesn't necessarily pay off: Reachability queries can often be answered even faster than single memory accesses in a precomputed full reachability matrix.