An extremely fast, exact algorithm for finding shortest paths in static networks with geographical background

Abstract

We present a new algorithm for fast and exact calculation of shortest paths in graphs with geometrical information stored at the nodes (coordinates), e.g., road networks. The method is based on pre-processing and therefore best suited for static graphs, i.e., graphs with fixed topology and edge costs. In the pre-processing phase, the network is divided into regions and edge flags are cal- culated that indicate whether an edge belongs to a shortest path into a given region. In the path calculation step, only those edges need to be investigated that carry the appro- priate flag. As compared to a classical Dijkstra implementation, we achieve an average speed-up of a factor of 64 on a European truck driver’s roadmap containing about 500000 road seg- ments. The concept of edge flags and how to use them in the path finding algorithm is discussed in this paper; the pre-processing step is just outlined. Results of both steps are presented for the above mentioned example.