Maximum weight matching

In computer science and graph theory, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights is maximized.

A special case of it is the assignment problem, in which the input is restricted to be a bipartite graph, and the matching constrained to be have cardinality that of the smaller of the two partitions. Another special case is the problem of finding a maximum cardinality matching on an unweighted graph: this corresponds to the case where all edge weights are the same.