Algorithm for Time-dependent Shortest Safe Path on Transportation Networks

Abstract

Abstract The shortest path problem in network has been studied widely and intensively over years. Many speed-up techniques for Dijkstra's algorithm have been developed. However, only few of those techniques work in time-dependent networks. This paper studies how to answer the shortest safe path between a pair of nodes over a large time-dependent transportation network, for typical applications, such as a heavy truck carrying inflammable materials, poison gas or explosive cargo, and traveling in a city. In this type of applications, a path is safe if the danger factor on each edge of the path is no more than a given upper bound. An efficient algorithm is proposed for finding the shortest safe path from source node to destination node when the starting time (departure time from the source) can be selected in a user-given starting-time interval. The proposed algorithm can provide optimal solution and the best starting time when a safe path exists in the given network. Also, it can find an approximate solution when the safe path does not exist. Moveover, our algorithm can handle both undirected and directed time-dependent network.