The transportation metric and related problems

The tranportation metric consisting of an undirected graph with positive edge weights proportional to travel time, and the problems related to the metric are discussed. The first optimal time algorithm for the construction of shortest path maps and Voronoi diagrams in this metric are also proposed. The complexity of this algorithm is lower than the quadratic worst case for classes of transportation networks such as clusters or uniform distribution of stations. In spite of these properties, the proposed transportation network cannot be modeled with weighted regions, but restricts entrance to and exit from the network to the fixed stations.