Levelwise Mesh Sparsification for Shortest Path Queries

In this paper, we address the shortest path query problem, i.e., constructing a data structure of a given network to answer the shortest path length of two given points in a short time. We present a method named Levelwise Mesh Sparsification for the problem. The key idea is to divide the network into meshes and to sparsify the network in each mesh by removing unnecessary edges and vertices that are never used when the shortest path passes through the mesh. In large real-world road networks in the United States, our method is about 1,500 times faster than Dijkstra’s algorithm, which is competitive with existing methods. The time taken to construct the data structure is a few hours on a typical PC. Unlike previous methods, our geometric partition method succeeded in reducing the data for connecting the sparsified network. As a result, our method uses additional data that is only about 10% of the original data size, while existing methods use more than 2000%. Our method has considerable extensibility because it is independent of search algorithms. Thus, it can be used with Dijkstra’s algorithm and A*-search among others, and with several models such as negative costs, time-dependent costs, and so on. These are rarely handled by previous methods.