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 language | English |
|---|---|
| Pages (from-to) | 2-17 |
| Number of pages | 16 |
| Journal | Journal of the Operations Research Society of Japan |
| Volume | 61 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2018 |
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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 journal › Article
}
TY - JOUR
T1 - A characterization of weighted popular matchings under matroid constraints
AU - Kamiyama, Naoyuki
PY - 2018/1
Y1 - 2018/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=85040356057&partnerID=8YFLogxK
U2 - 10.15807/jorsj.61.2
DO - 10.15807/jorsj.61.2
M3 - Article
AN - SCOPUS:85040356057
VL - 61
SP - 2
EP - 17
JO - Journal of the Operations Research Society of Japan
JF - Journal of the Operations Research Society of Japan
SN - 0453-4514
IS - 1
ER -