PReaCH: A Fast Lightweight Reachability Index Using Pruning and Contraction Hierarchies.

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly simple and guarantees linear space and near linear preprocessing time. Orthogonally to that, we improve existing pruning techniques for the search by gathering more information from a single DFS-traversal of the graph. In particular, we show that more classes of node numberings can be used to obtain strong pruning information.