Abstract Summary of results The subcubic (O(n ) for < 3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C = AB but if Cij = 1 they d...
Let G = (V, E, w) be a directed graph, where w : V → R is an arbitrary weight function defined on its vertices. The bottleneck weight, or the capacity, of a path is the smalles...
Let G be a directed edge-weighted graph and let P be a shortest path from s to t in G. The replacement paths problem asks to compute, for every edge e on P, the shortest s-to-t pat...
Let G = (V, E) be an weighted undirected graph on n vertices and m edges, and let dG be its shortest path metric. We present two simple deterministic algorithms for approximating ...