Pareto stable matchings under one-sided matroid constraints

Research output: Contribution to journalArticle

Abstract

The Pareto stability is one of the solution concepts in two-sided matching markets with ties. It is known that there always exists a Pareto stable matching in the many-to-many setting. In this paper, we consider the following generalization of the Pareto stable matching problem in the many-to-many setting. Each agent v of one side has a matroid defined on the set of edges incident to v, and the set of edges assigned to v must be an independent set of this matroid. By extending the algorithm of Kamiyama for the many-to-many setting, we prove that there always exists a Pareto stable matching in this setting, and a Pareto stable matching can be found in polynomial time.

Original languageEnglish
Pages (from-to)1431-1451
Number of pages21
JournalSIAM Journal on Discrete Mathematics
Volume33
Issue number3
DOIs
Publication statusPublished - Jan 1 2019

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Stable Matching
Matroid
Pareto
Many to many
Solution Concepts
Matching Problem
Tie
Independent Set
Polynomial time

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Pareto stable matchings under one-sided matroid constraints. / Kamiyama, Naoyuki.

In: SIAM Journal on Discrete Mathematics, Vol. 33, No. 3, 01.01.2019, p. 1431-1451.

Research output: Contribution to journalArticle

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