Reduce matrix
Subtract row min from each row. Subtract col min from each col. Zeros identify potential matches.
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Alternating trees
Grow trees from unmatched vertices via zero-cost edges. Augment when path found.
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Dual variables
Potentials on left + right vertices. Adjust to expose new zeros as needed.
Complexity
Classic Kuhn-Munkres: O(V³). Modern implementations achieve O(V³) crisply.