The e-approximation of the Label Correcting Modification of the Dijkstra's Algorithm

This paper is focused on searching the shortest paths for all departure times (profile search). This problem is called a time-dependent shortest path problem (TDSP) and is important for optimization in transportation. Particularly this paper deals with the ε-approximation of TDSP. The proposed algorithm is based on a label correcting modification of Dijkstra's algorithm (LCA). The main idea of the algorithm is to simplify the arrival function after every relaxation step so that the maximum relative error is maintained. When the maximum relative error is 0.001, the proposed solution saves more than 95% of breakpoints and 80% time compared to the exact version of LCA. A more efficient precomputation step for another time-dependent routing algorithms can be built using the developed algorithm.