Efficient fastest-path computations for road maps

In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a “travel time” value, are becoming a standard feature of many navigation-related applications. To support this, very efficient computation of these paths in very large road networks is critical. Fastest paths may be computed as minimal-cost paths in a weighted directed graph, but traditional minimal-cost path algorithms based on variants of the classical Dijkstra algorithm do not scale well, as in the worst case they may traverse the entire graph. A common improvement, which can dramatically reduce the number of graph vertices traversed, is the A* algorithm, which requires a good heuristic lower bound on the minimal cost. We introduce a simple, but very effective, heuristic function based on a small number of values assigned to each graph vertex. The values are based on graph separators and are computed efficiently in a preprocessing stage. We present experimental results demonstrating that our heuristic provides estimates of the minimal cost superior to those of other heuristics. Our experiments show that when used in the A* algorithm, this heuristic can reduce the number of vertices traversed by an order of magnitude compared to other heuristics.