Matchings with Lower Quotas: Algorithms and Complexity
نویسندگان
چکیده
منابع مشابه
Many-to-one Matchings with Lower Quotas: Algorithms and Complexity
We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = (A∪̇P,E) with weights on the edges in E, and with lower and upper quotas on the vertices in P . We seek a maximum weight many-toone matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either ...
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We consider the well-studied Hospital Residents (HR) problem in the presence of lower quotas (LQ). The input instance consists of a bipartite graph G = (R∪H, E) where R and H denote sets of residents and hospitals respectively. Every vertex has a preference list that imposes a strict ordering on its neighbors. In addition, each hospital h has an associated upper-quota q+(h) and lower-quota q−(h...
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While every instance of the Hospitals/Residents problem admits a stable matching, the problem with lower quotas (HR-LQ) has instances with no stable matching. For such an instance, we expect the existence of an envy-free matching, which is a relaxation of a stable matching preserving a kind of fairness property. In this paper, we investigate the existence of an envy-free matching in several set...
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We consider the problem of allocating applicants to courses, where each applicant has a capacity, possibly greater than 1, and a subset of acceptable courses that she ranks in strict order of preference. Each course has a lower and an upper quota, indicating that if it is assigned some applicants then their number has to be between these two bounds. We further suppose that applicants extend the...
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Classified stable matching, proposed by Huang, describes a matching model between academic institutes and applicants, where each institute has upper and lower quotas on classes, i.e., subsets of applicants. Huang showed that the problem to decide whether there exists a stable matching or not is NP-hard in general. On the other hand, he showed that the problem is solvable if the classes form a l...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2016
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-016-0252-6