The popular matching and condensation problems under matroid constraints

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The popular matching problem introduced by Abraham, Irving, Kavitha, and Mehlhorn is a matching problem in which there exist applicants and posts, and applicants have preference lists over posts. A matching M is said to be popular, if there exists no other matching N such that the number of applicants that prefer N to M is larger than the number of applicants that prefer M to N. The goal of this problem is to decide whether there exists a popular matching, and find a popular matching if one exists. In this paper, we first consider a matroid generalization of the popular matching problem with strict preference lists, and give a polynomial-time algorithm for this problem. In the second half of this paper, we consider the problem of transforming a given instance of a matroid generalization of the popular matching problem with strict preference lists by deleting a minimum number of applicants so that it has a popular matching. This problem is a matroid generalization of the popular condensation problem with strict preference lists introduced by Wu, Lin, Wang, and Chao. By using the results in the first half, we give a polynomial-time algorithm for this problem.

Original languageEnglish
Pages (from-to)1305-1326
Number of pages22
JournalJournal of Combinatorial Optimization
Volume32
Issue number4
DOIs
Publication statusPublished - Nov 1 2016

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Matroid
Condensation
Matching Problem
Polynomials
Polynomial-time Algorithm
Generalization

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

The popular matching and condensation problems under matroid constraints. / Kamiyama, Naoyuki.

In: Journal of Combinatorial Optimization, Vol. 32, No. 4, 01.11.2016, p. 1305-1326.

Research output: Contribution to journalArticle

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