Route planning in a weakly dynamic undirected graph

In this paper, we study weakly dynamic undirected graphs, and we propose an efficient polynomial algorithm that computes in advance alternative shortest paths for all possible configurations. No additional computation is then needed after any change in the problem because shortest paths are already known in all cases. We use these results to compute critical values for the traversal duration and to pre-compute best paths, and we apply this result to one delivery problem for trucks from one regional storehouse to several local stores when one possible point has a variable traversal duration.