O’Reach: Even Faster Reachability in Large Graphs

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.