### Abstract

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.

Original language | English |
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Title of host publication | Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 |

Pages | 135-142 |

Number of pages | 8 |

Publication status | Published - Apr 30 2012 |

Externally published | Yes |

Event | 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 - Kyoto, Japan Duration: Jan 17 2012 → Jan 19 2012 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 |
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Country | Japan |

City | Kyoto |

Period | 1/17/12 → 1/19/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012*(pp. 135-142). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

**A matroid approach to stable matchings with lower quotas.** / Fleiner, Tamás; Kamiyama, Naoyuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012.*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 135-142, 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, 1/17/12.

}

TY - GEN

T1 - A matroid approach to stable matchings with lower quotas

AU - Fleiner, Tamás

AU - Kamiyama, Naoyuki

PY - 2012/4/30

Y1 - 2012/4/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84860119976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860119976&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84860119976

SN - 9781611972108

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 135

EP - 142

BT - Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012

ER -