A matroid approach to stable matchings with lower quotas

Tamás Fleiner, Naoyuki Kamiyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

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 languageEnglish
Title of host publicationProceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
Pages135-142
Number of pages8
Publication statusPublished - Apr 30 2012
Externally publishedYes
Event23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 - Kyoto, Japan
Duration: Jan 17 2012Jan 19 2012

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
CountryJapan
CityKyoto
Period1/17/121/19/12

Fingerprint

Stable Matching
Matroid
Polynomials
Matching Problem
Assignment
Lattice Structure
Upper and Lower Bounds
Polynomial time

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Cite this

Fleiner, T., & Kamiyama, N. (2012). A matroid approach to stable matchings with lower quotas. In 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.

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Fleiner, T & Kamiyama, N 2012, A matroid approach to stable matchings with lower quotas. in 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.
Fleiner T, Kamiyama N. A matroid approach to stable matchings with lower quotas. In Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012. 2012. p. 135-142. (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).
Fleiner, Tamás ; Kamiyama, Naoyuki. / A matroid approach to stable matchings with lower quotas. Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012. 2012. pp. 135-142 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).
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