Let G=(V,E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe an \tilde{O}(min{n^{3/2}m^{1/2},n^{7/3}) time ... more >>>

We present two new algorithms for solving the {\em All Pairs Shortest Paths\/} (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in $\Ot(n^{2+\mu})$ ... more >>>