One of many initially polynomial-time algorithms for well balanced assignment was the Hungarian algorithm. It really is a world algorithm – it is based on improving a matching alongside augmenting paths (alternating paths concerning unmatched vertices).
To ensure which the variables without a doubt characterize a wonderful matching, we increase constraints saying that every vertex is adjacent to accurately just one edge within the matching, i.
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new edges are essential. The ensuing graph constantly has a wonderful matching of measurement n + r displaystyle n+r
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