Maximum cardinality popular matchings in the stable marriage problem
نویسندگان
چکیده
Popular matching and was extensively studied in recent years as an alternative to stable matchings. Both type of matchings are defined in the framework of Stable Marriage (SM) problem: in a given bipartite graph G = (A,B;E) each vertex u has a strict order of preference on its neighborhood. A matching M is popular, if for every matching M ′ of G, the number of vertices that prefer M ′ to M is at most the number of vertices which prefer M to M ′. In this paper we prove that every maximum cardinality popular matching saturates the same set of vertices. This property is similar to that of stable matchings: any such matching saturates the same set of vertices.
منابع مشابه
Popular Matchings in the Stable Marriage Problem
The input is a bipartite graph G = (A ∪B ,E) where each vertex u ∈ A ∪B ranks its neighbors in a strict order of preference. This is the same as an instance of the stable marriage problem with incomplete lists. A matching M∗ is said to be popular if there is no matching M such that more vertices are better off in M than in M∗. Any stable matching of G is popular, however such a matching is a mi...
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