Route planning in dynamic graphs with linear changing and preprocessing for speed-up

The goal of this paper is to work out a concept for route planning in a road network, where the costs of roads are not constant, but changing in a linear way. The solution developed is based on the classical Dijkstra's algorithm, which helps to find the route with minimal cost. The new algorithm takes the varying into account in order to find out the best route. This search refers not only to a moment of the departure but to the whole duration of the travel. A speed-up technique has been developed for preprocessing before run time. This preprocessing phase helps to give back the route with minimal cost for the user quickly in run time query. A numerical example has been presented to show the detailed steps of the algorithm and the speed-up technique.