Popular Matchings with Multiple Partners
نویسندگان
چکیده
Our input is a bipartite graph G = (R ∪ H,E) where each vertex in R ∪ H has a preference list strictly ranking its neighbors. The vertices in R (similarly, in H) are called residents (resp., hospitals): each resident seeks to be matched to a hospital while each hospital h seeks cap(h) ≥ 1 many residents to be matched to it. The Gale-Shapley algorithm computes a stable matching in G in linear time. We consider the problem of computing a popular matching in G – a matching M is popular if M cannot lose an election to any other matching where vertices cast votes for one matching versus another. Our main contribution is to show that a max-size popular matching in G can be computed by the 2-level Gale-Shapley algorithm in linear time. This is a simple extension of the classical Gale-Shapley algorithm and we prove its correctness via linear programming.
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