Data Structures for Weighted Matching and Extensions to b-matching and f-factors

@article{Gabow2018DataSF,
title={Data Structures for Weighted Matching and Extensions to b-matching and f-factors},
author={Harold N. Gabow},
journal={ACM Trans. Algorithms},
year={2018},
volume={14},
pages={39:1-39:80}
}

This article shows the weighted matching problem on general graphs can be solved in time <i>O</i>(<i>n</i>(<i>m</i> + <i>n</i> log <i>n</i>)) for <i>n</i> and <i>m</i> the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a data structure for blossom creation. It uses a dynamic nearest-common-ancestor algorithm to simplify blossom steps, so they involve only back edges rather than arbitrary nontree edges.
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