We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental singlesource shortest-paths...
We obtain the first approximation algorithm for finding the k-simple shortest paths connecting a pair of vertices in a weighted directed graph. Our algorithm is deterministic an...
We define general algebraic frameworks for shortest-distance problems based on the structure of semirings. We give a generic algorithm for finding single-source shortest distances...
We present a simple space saving trick that applies to many previous algorithms for transitive closure and shortest paths in dynamic directed graphs. In these problems, an update c...
Let D be a weighted directed graph cellularly embedded in a surface of genus g, orientable or not, possibly with boundary. We describe algorithms to compute a shortest non-contrac...