Fast Approximations for Rooted Connectivity in Weighted Directed Graphs

Abstract: We consider approximations for computing minimum weighted cuts in directed graphs. We consider both rooted and global minimum cuts, and both edge-cuts and vertex-cuts. For these problems we give randomized Monte Carlo algorithms that compute a $(1+\epsilon)$-approximate minimum cut in $\tilde{O}(n^2 / \epsilon^2)$ time. These results extend and build on recent work [4] that obtained exact algorithms with similar running times in directed graphs with small integer capacities.