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How can I find imperfect bipartite chart matching?

That is, how can I find a bipartite graph match where some vertices cannot be connected to any other vertices?

EDIT: Another condition, suppose the edges are also weighted, and I would like the match to be such that the total edge weight is minimized (or maximized).

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2 answers

First, I'm going to suggest that your weights are non-negative.

: n , . , . , 0 , , 0 , / . , , , . . , " " , .

: , , . . 0 , .

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Hopcroft-Karp, , .

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