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.
|ジャーナル||Journal of the Operations Research Society of Japan|
|出版物ステータス||出版済み - 1 2018|
All Science Journal Classification (ASJC) codes
- Decision Sciences(all)
- Management Science and Operations Research