A characterization of weighted popular matchings under matroid constraints

Research output: Contribution to journalArticle

Abstract

The popular matching problem introduced by Abraham, Irving, Kavitha, and Mehlhorn is one of bipartite matching problems with one-sided preference lists. In this paper, we first propose a matroid generalization of the weighted variant of popular matchings introduced by Mestre. Then we give a characterization of weighted popular matchings in bipartite graphs with matroid constraints and one-sided preference lists containing no ties. This characterization is based on the characterization of weighted popular matchings proved by Mestre. Lastly we prove that we can decide whether a given matching is a weighted popular matching under matroid constraints in polynomial time by using our characterization.

Original languageEnglish
Pages (from-to)2-17
Number of pages16
JournalJournal of the Operations Research Society of Japan
Volume61
Issue number1
DOIs
Publication statusPublished - Jan 2018

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Matching problem
Bipartite graph
Polynomials

All Science Journal Classification (ASJC) codes

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

Cite this

A characterization of weighted popular matchings under matroid constraints. / Kamiyama, Naoyuki.

In: Journal of the Operations Research Society of Japan, Vol. 61, No. 1, 01.2018, p. 2-17.

Research output: Contribution to journalArticle

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