The.Algorithm.Design.Manual.Springer-Verlag.1998

Matching
Combinatorica [Ski90] provides a (slow) Mathematica implementations of bipartite and maximal
matching, as well as the stable marriage theorem. See Section .
Notes: Lovász and Plummer [LP86] is the definitive reference on matching theory and algorithms.
Survey articles on matching algorithms include [Gal86]. Good expositions on network flow algorithms
for bipartite matching include [CLR90, Eve79a, Man89], and those on the Hungarian method include
[Law76, PS82]. The best algorithm for maximum bipartite matching, due to Hopcroft and Karp [HK73],
repeatedly finds the shortest augmenting paths instead of using network flow, and runs in .
Expositions on the augmenting path method include [Man89, PS82, SDK83].
Edmond's algorithm [Edm65] for maximum-cardinality matching is of great historical interest for
provoking questions about what problems can be solved in polynomial time. Expositions on Edmond's
algorithm include [Law76, PS82, Tar83]. Gabow's [Gab76] implementation of Edmond's algorithm runs
in time. The best algorithm known for general matching runs in [MV80]. A faster
algorithm for matching in geometic graphs appears in [Vai88].
The theory of stable matching is thoroughly treated in [GI89]. The original algorithm for finding stable
marriages is due to Gale and Shapely [GS62] with expositions including [Law76].
Related Problems: Eulerian cycle (see page ), network flow (see page ).
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and Reduction
Algorithms
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