The blossom algorithm finds a maximum independent edge set in a (possibly weighted) graph. While a maximum independent edge set can be found fairly easily for a bipartite graph using the Hungarian maximum matching algorithm, the general case is more difficult. Edmonds's blossom algorithm starts with a maximal independent edge set, which it tries to extend to a maximum independent edge set using the property that a matching is maximum iff the matching does not admit an augmenting path.
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