We propose an algorithm which reoptimizes shortest paths in a very general situation, that is when any subset of arcs of the input graph is aected by a change of the arc costs, which can be either lower or higher than the old ones. This situation is more general than the ones addressed in the literature so far.

Let G =(V,E,w) be a simple digraph, in which all edge weights are non-negative real numbers. Let G ′ be obtained from G by the application of a set of edge weight updates to G. Lets∈V, and let Ts and T ′ s be a Shortest Path Tree (SPT) rooted at s in G and G ′ , respectively. The Dynamic Shortest Path (DSP) problem is to compute T ′ s from Ts. For the DSP problem, we correct and extend a few existing SPT algorithms to handle multiple edge weight updates. We prove that these extended algorithms are correct. The complexity of these algorithms is also analyzed. To evaluate the proposed algorithms, we compare them with the well-known static Dijkstra algorithm. Extensive experiments are conducted with both real-life and artificial data sets. The real-life data are road system graphs obtained from the Connecticut road system and are relatively sparse. The artificial data are randomly generated graphs and are relatively dense. The experimental results suggest the most appropriate algorithms to be used under different circumstances.