A balancing-weights technique lets a randomized augmenting-paths algorithm compute max flow in directed graphs in m + nF time, matching the undirected case.
Maximum bipartite matching in n^ 2+o(1) time via a combinatorial algorithm
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Balancing Weights, Directed Sparsification, and Augmenting Paths
A balancing-weights technique lets a randomized augmenting-paths algorithm compute max flow in directed graphs in m + nF time, matching the undirected case.