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- W2037078275 abstract "We consider the problem of computing a maximum cardinality popular matching in a bipartite graph G = ( A ∪ B , E ) where each vertex u ∈ A ∪ B ranks its neighbors in a strict order of preference. Such a graph is called an instance of the stable marriage problem with strict preferences and incomplete lists. A matching M ⁎ is popular if for every matching M in G , the number of vertices that prefer M to M ⁎ is at most the number of vertices that prefer M ⁎ to M . Every stable matching of G is popular, however a stable matching is a minimum cardinality popular matching. The complexity of computing a maximum cardinality popular matching was unknown. In this paper we show a simple characterization of popular matchings in G = ( A ∪ B , E ) . We also show a sufficient condition for a popular matching to be a maximum cardinality popular matching. We construct a matching that satisfies our characterization and sufficient condition in O ( m n 0 ) time, where m = | E | and n 0 = min ( | A | , | B | ) . Thus the maximum cardinality popular matching problem in G = ( A ∪ B , E ) can be solved in O ( m n 0 ) time." @default.
- W2037078275 created "2016-06-24" @default.
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- W2037078275 date "2013-01-01" @default.
- W2037078275 modified "2023-09-29" @default.
- W2037078275 title "Popular matchings in the stable marriage problem" @default.
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- W2037078275 doi "https://doi.org/10.1016/j.ic.2012.10.012" @default.
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