The computation of point-to-point shortest paths on time-dependent road networks has a large practical interest, but very few works propose efficient algorithms for this problem. We propose a novel approach which tackles one of the main complications of route planning in time-dependent graphs, which is the difficulty of using bidirectional search: since the exact arrival time at the destination is unknown, we start a backward search from the destination node using lower bounds on arc costs in order to restrict the set of nodes that have to be explored by the forward search. Our algorithm is based on A* with landmarks (ALT); extensive computational results show that it is very effective in practice if we are willing to accept a small approximation factor, resulting in a speed-up of several times with respect to Dijkstra’s algorithm while finding only slightly suboptimal solutions. The main idea presented here can also be generalized to other types of search algorithms.
Unpublished: LIX, Ecole Polytechnique, F-91128 Palaiseau, France. May 2008.