A randomized algorithm computes the weighted global minimum vertex-cut in O(min{mn^{0.99+o(1)}, m^{1.5+o(1)}}) time, breaking the long-standing O~(mn) barrier.
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Breaking the O(mn)-Time Barrier for Vertex-Weighted Global Minimum Cut
A randomized algorithm computes the weighted global minimum vertex-cut in O(min{mn^{0.99+o(1)}, m^{1.5+o(1)}}) time, breaking the long-standing O~(mn) barrier.