The lattice structure of the set of stable matchings with multiple partners
Mathematics of Operations Research
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Characterization of stable matchings as extreme points of a polytope
Mathematical Programming: Series A and B
A Matroid Generalization of the Stable Matching Polytope
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
A fixed-point approach to stable matchings and some applications
Mathematics of Operations Research
The College Admissions problem with lower and common quotas
Theoretical Computer Science
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The hospitals/residents problem with quota lower bounds
ESA'11 Proceedings of the 19th European conference on Algorithms
Complementary cooperation, minimal winning coalitions, and power indices
Theoretical Computer Science
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In SODA'10, Huang introduced the laminar classified stable matching problem (LCSM for short) that is motivated by academic hiring. This problem is an extension of the well-known hospitals/residents problem in which a hospital has laminar classes of residents and it sets lower and upper bounds on the number of residents that it would hire in that class. Against the intuition that stable matching problems with lower quotas are difficult in general, Huang proved that this problem can be solved in polynomial time. In this paper, we propose a matroid-based approach to this problem and we obtain the following results. (i) We solve a generalization of the LCSM problem. (ii) We exhibit a polyhedral description for stable assignments of the LCSM problem, which gives a positive answer to Huang's question. (iii) We prove that the set of stable assignments of the LCSM problem has a lattice structure similarly to the ordinary stable matching model.