Forward search in contraction hierarchies

Contraction hierarchies are graph-based data structures developed to speed up shortest path search in road networks. Built during an offline pre-processing step, contraction hierarchies are always paired with an online query algorithm which is a variation on bi-directional Dijkstra search. Though effective and highly popular this combination can sometimes be difficult to extend, for example in order to leverage goal-directed heuristics or other forward-driven pruning techniques. In this paper we deconstruct the bi-directional query algorithm of contraction hierarchies and derive a new algorithmic schema which is compatible with standard unidirectional or bi-directional search. We then develop a variety of new uni-directional query algorithms to find optimal paths in contraction hierarchies. These are based on the combination of A* search and Geometric Containers, a well known and successful edge-pruning technique. Empirical results show that our approach can improve search times by an order of magnitude vs bi-directional Dijkstra, albeit at the cost of additional memory and pre-processing time.