Construction
1. Find max matching. 2. Let U = unmatched left vertices. 3. Alternating BFS from U: even level via matching, odd via non-matching. 4. Cover = (left \ visited) ∪ (right ∩ visited).
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Complexity
Max matching: O(E·√V). Cover extraction: O(V+E). Total: O(E·√V).
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Independent set
Complement of vertex cover is independent set. Bipartite max indep set = V - min vertex cover.
Applications
Job scheduling. Facility placement. Any bipartite conflict minimization.