Popular matchings in the weighted capacitated house allocation problem
نویسندگان
چکیده
منابع مشابه
Popular matchings in the weighted capacitated house allocation problem
We consider the problem of finding a popular matching in the Weighted Capacitated House Allocation problem (WCHA). An instance of WCHA involves a set of agents and a set of houses. Each agent has a positive weight indicating his priority, and a preference list in which a subset of houses are ranked in strict order. Each house has a capacity that indicates the maximum number of agents who could ...
متن کاملPopular Matchings in the Capacitated House Allocation Problem
We consider the problem of finding a popular matching in the Capacitated House Allocation problem (CHA). An instance of CHA involves a set of agents and a set of houses. Each agent has a preference list in which a subset of houses are ranked in strict order, and each house may be matched to a number of agents that must not exceed its capacity. A matching M is popular if there is no other matchi...
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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...
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For a set A of n applicants and a set I of m items, let us consider the problem of matching applicants to items, where each applicant x ∈ A provides its preference list defined on items. We say that an applicant x prefers an item p than an item q if p is located at higher position than q in its preference list. For any matchingsM andM′ of the matching problem, we say that an applicant x prefers...
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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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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2010
ISSN: 1570-8667
DOI: 10.1016/j.jda.2008.11.008