Minimum cost path in time-dependent graph

In this paper, the time dependent graph is presented. We propose search several fast algorithms, which allow us to define minimal time cost path and minimal cost path. The proposed method is based on an adaptation of the Dijskstra and A^* algorithms. Some extensions concerning an evolution where the cost changes in the path is also discussed. To search the optimal path, we compare the results obtained from an A^* algorithm, and dynamic programming algorithm.