Computing Many-to-Many Shortest Paths Using Highway Hierarchies

We present a fast algorithm for computing all shortest paths between source nodes s ∈ S and target nodes t ∈ T . This problem is important as an initial step for many operations research problems (e.g., the vehicle routing problem), which require the distances between S and T as input. Our approach is based on highway hierarchies, which are also used for the currently fastest speedup techniques for shortest path queries in road networks. We show how to use highway hierarchies so that for example, a 10 000× 10 000 distance table in the European road network can be computed in about one minute. These results are based on a simple basic idea, several refinements, and careful engineering of the approach. We also explain how the approach can be parallelized and how the computation can be restricted to computing only the k closest connections.