A memory efficient reachability data structure through bit vector compression

When answering many reachability queries on a large graph, the principal challenge is to represent the transitive closure of the graph compactly, while still allowing fast membership tests on that transitive closure. Recent attempts to address this problem are complex data structures and algorithms such as Path-Tree and 3-HOP. We propose a simple alternative based on a novel form of bit-vector compression. Our starting point is the observation that when computing the transitive closure, reachable vertices tend to cluster together. We adapt the well-known scheme of word-aligned hybrid compression (WAH) to work more efficiently by introducing word partitions. We prove that the resulting scheme leads to a more compact data structure than its closest competitor, namely interval lists. In extensive and detailed experiments, this is confirmed in practice. We also demonstrate that the new technique can handle much larger graphs than alternative algorithms.