Many-to-many stable matchings with ties in trees

Keita Nakamura, Naoyuki Kamiyama

Research output: Contribution to journalArticle

Abstract

In the stable matching problem introduced by Gale and Shapley, it is known that in the case where the preference lists may involve ties, a stable matching always exists, but the sizes of stable matchings may be different. In this paper, we consider the problem of finding a maximum-size stable matching in a many-to-many matching market with ties. It is known that this problem is NP-hard even if the capacity of every agent is one. In this paper, we prove that this problem in trees can be solved in polynomial time by extending the algorithm proposed by Tayu and Ueno for the one-to-one setting.

Original languageEnglish
Pages (from-to)225-240
Number of pages16
JournalJournal of the Operations Research Society of Japan
Volume59
Issue number3
DOIs
Publication statusPublished - Jan 1 2016

Fingerprint

Stable matching
Matching problem
NP-hard
Matching markets
Polynomials

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research

Cite this

Many-to-many stable matchings with ties in trees. / Nakamura, Keita; Kamiyama, Naoyuki.

In: Journal of the Operations Research Society of Japan, Vol. 59, No. 3, 01.01.2016, p. 225-240.

Research output: Contribution to journalArticle

@article{11124e28d4a14e94a895d570ec48a4e4,
title = "Many-to-many stable matchings with ties in trees",
abstract = "In the stable matching problem introduced by Gale and Shapley, it is known that in the case where the preference lists may involve ties, a stable matching always exists, but the sizes of stable matchings may be different. In this paper, we consider the problem of finding a maximum-size stable matching in a many-to-many matching market with ties. It is known that this problem is NP-hard even if the capacity of every agent is one. In this paper, we prove that this problem in trees can be solved in polynomial time by extending the algorithm proposed by Tayu and Ueno for the one-to-one setting.",
author = "Keita Nakamura and Naoyuki Kamiyama",
year = "2016",
month = "1",
day = "1",
doi = "10.15807/jorsj.59.225",
language = "English",
volume = "59",
pages = "225--240",
journal = "Journal of the Operations Research Society of Japan",
issn = "0453-4514",
publisher = "Operations Research Society of Japan",
number = "3",

}

TY - JOUR

T1 - Many-to-many stable matchings with ties in trees

AU - Nakamura, Keita

AU - Kamiyama, Naoyuki

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In the stable matching problem introduced by Gale and Shapley, it is known that in the case where the preference lists may involve ties, a stable matching always exists, but the sizes of stable matchings may be different. In this paper, we consider the problem of finding a maximum-size stable matching in a many-to-many matching market with ties. It is known that this problem is NP-hard even if the capacity of every agent is one. In this paper, we prove that this problem in trees can be solved in polynomial time by extending the algorithm proposed by Tayu and Ueno for the one-to-one setting.

AB - In the stable matching problem introduced by Gale and Shapley, it is known that in the case where the preference lists may involve ties, a stable matching always exists, but the sizes of stable matchings may be different. In this paper, we consider the problem of finding a maximum-size stable matching in a many-to-many matching market with ties. It is known that this problem is NP-hard even if the capacity of every agent is one. In this paper, we prove that this problem in trees can be solved in polynomial time by extending the algorithm proposed by Tayu and Ueno for the one-to-one setting.

UR - http://www.scopus.com/inward/record.url?scp=84982994477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982994477&partnerID=8YFLogxK

U2 - 10.15807/jorsj.59.225

DO - 10.15807/jorsj.59.225

M3 - Article

AN - SCOPUS:84982994477

VL - 59

SP - 225

EP - 240

JO - Journal of the Operations Research Society of Japan

JF - Journal of the Operations Research Society of Japan

SN - 0453-4514

IS - 3

ER -