Popular Matchings
نویسنده
چکیده
منابع مشابه
Two-sided popular matchings in bipartite graphs with forbidden/forced elements and weights
Two-sided popular matchings in bipartite graphs are a well-known generalization of stable matchings in the marriage setting, and they are especially relevant when preference lists are incomplete. In this case, the cardinality of a stable matching can be as small as half the size of a maximum matching. Popular matchings allow for assignments of larger size while still guaranteeing a certain fair...
متن کاملPopular Mixed Matchings
We study the problem of matching applicants to jobs under one-sided preferences; that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties. A matching M is said to be more popular than T if the applicants that prefer M to T outnumber those that prefer T to M . A matching is said to be popular if there is no matching more popular than it. Equi...
متن کاملCharacterizing a Set of Popular Matchings Defined by Preference Lists with Ties
In this paper, we give a characterization of a set of popular matchings in a bipartite graph with one-sided preference lists. The concept of a popular matching was first introduced by Gardenfors [5]. Recently, Abraham et al. [1] discussed a problem for finding a popular matching and proposed polynomial time algorithms for problem instances defined by preference lists with or without ties. McDer...
متن کاملCounting Popular Matchings in House Allocation Problems
We study the problem of counting the number of popular matchings in a given instance. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an...
متن کاملMaximum cardinality popular matchings in the stable marriage problem
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 a...
متن کاملPopularity, Mixed Matchings, and Self-duality
Our input instance is a bipartite graph G = (A∪B,E) where A is a set of applicants, B is a set of jobs, and each vertex u ∈ A∪B has a preference list ranking its neighbors in a strict order of preference. For any two matchings M and T in G, let φ(M,T ) be the number of vertices that prefer M to T . A matching M is popular if φ(M,T )≥ φ(T,M) for all matchings T in G. There is a utility function ...
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