In the previous chapter, we studied matchings of maximal cardinality (the cardinality matching problem). The present chapter is devoted to weighted matchings, in particular to the problem of finding a matching of maximal weight in a network (G,w) (the weighted matching problem). In the bipartite case, this problem is equivalent to the assignment problem introduced in Example 10.1.4, so that the methods discussed in Chapter 10 apply. Nevertheless, we will give a further algorithm for the bipartite case, the Hungarian algorithm, which is one of the best known and most important combinatorial algorithms.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Weighted matchings. In: Graphs, Networks and Algorithms. Algorithms and Computation in Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72780-4_14
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DOI: https://doi.org/10.1007/978-3-540-72780-4_14
Publisher Name: Springer, Berlin, Heidelberg
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