  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.
