Fast Approximations for Rooted Connectivity in Weighted Directed Graphs

04/14/2021

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by   Kent Quanrud, et al.

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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+ϵ)-approximate minimum cut in Õ(n^2 / ϵ^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.