Faster Reachability in Static Graphs

08/25/2020

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by   Kathrin Hanauer, et al.

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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. In an experimental study, we compare a variety of algorithms with respect to their index-building and query times as well as their memory footprint. All of them yield a time/space trade-off for queries. Surprisingly, due to cache effects, a higher investment in space doesn't necessarily pay off: Reachability queries can often be answered even significantly faster than single memory accesses in a precomputed full reachability matrix.