矩阵约束下加权流行匹配的刻画

Q4 Decision Sciences

Journal of the Operations Research Society of Japan Pub Date : 2018-01-01 DOI:10.15807/JORSJ.61.2

Naoyuki Kamiyama

{"title":"矩阵约束下加权流行匹配的刻画","authors":"Naoyuki Kamiyama","doi":"10.15807/JORSJ.61.2","DOIUrl":null,"url":null,"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.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"61 1","pages":"2-17"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.2","citationCount":"1","resultStr":"{\"title\":\"A characterization of weighted popular matchings under matroid constraints\",\"authors\":\"Naoyuki Kamiyama\",\"doi\":\"10.15807/JORSJ.61.2\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":51107,\"journal\":{\"name\":\"Journal of the Operations Research Society of Japan\",\"volume\":\"61 1\",\"pages\":\"2-17\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.15807/JORSJ.61.2\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Operations Research Society of Japan\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15807/JORSJ.61.2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Decision Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Operations Research Society of Japan","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15807/JORSJ.61.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Decision Sciences","Score":null,"Total":0}

引用次数: 1

摘要

Abraham, Irving, Kavitha, Mehlhorn等人提出的比较流行的匹配问题是带有片面偏好表的二部匹配问题。在本文中，我们首先提出了Mestre引入的流行匹配的加权变体的矩阵泛化。然后给出了具有矩阵约束的二部图和不含联系的单侧偏好表的加权流行匹配的刻画。这种表征是基于Mestre证明的加权流行匹配的表征。最后，我们证明了在多项式时间内可以判定给定匹配是否为矩阵约束下的加权流行匹配。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A characterization of weighted popular matchings under matroid constraints

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the Operations Research Society of Japan 管理科学-运筹学与管理科学

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The journal publishes original work and quality reviews in the field of operations research and management science to OR practitioners and researchers in two substantive categories: operations research methods; applications and practices of operations research in industry, public sector, and all areas of science and engineering.