多样化的配对

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING Algorithmica Pub Date : 2024-03-15 DOI:10.1007/s00453-024-01214-7

Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, Danil Sagunov

{"title":"多样化的配对","authors":"Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, Danil Sagunov","doi":"10.1007/s00453-024-01214-7","DOIUrl":null,"url":null,"abstract":"<div>We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse Pair of Matchings (asking for two not necessarily maximum or perfect matchings) is \\(\\textsf{NP}\\)-complete on general graphs if k is part of the input, and we consider two restricted variants. First, we show that on bipartite graphs, the problem is polynomial-time solvable, and second we show that Diverse Pair of Maximum Matchings is \\(\\textsf{FPT}\\) parameterized by k. We round off the work by showing that Diverse Pair of Matchings has a kernel on \\({\\mathcal {O}}(k^2)\\) vertices.</div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 6","pages":"2026 - 2040"},"PeriodicalIF":0.9000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01214-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Diverse Pairs of Matchings\",\"authors\":\"Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, Danil Sagunov\",\"doi\":\"10.1007/s00453-024-01214-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse Pair of Matchings (asking for two not necessarily maximum or perfect matchings) is \\\\(\\\\textsf{NP}\\\\)-complete on general graphs if k is part of the input, and we consider two restricted variants. First, we show that on bipartite graphs, the problem is polynomial-time solvable, and second we show that Diverse Pair of Maximum Matchings is \\\\(\\\\textsf{FPT}\\\\) parameterized by k. We round off the work by showing that Diverse Pair of Matchings has a kernel on \\\\({\\\\mathcal {O}}(k^2)\\\\) vertices.</div>\",\"PeriodicalId\":50824,\"journal\":{\"name\":\"Algorithmica\",\"volume\":\"86 6\",\"pages\":\"2026 - 2040\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00453-024-01214-7.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algorithmica\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00453-024-01214-7\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algorithmica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00453-024-01214-7","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}

引用次数: 0

摘要

我们开始研究"（最大/完美）匹配的多样性对"（Diverse Pair of (Maximum/ Perfect) Matchings）问题，给定一个图 G 和一个整数 k，问 G 是否有两个对称差至少为 k 的（最大/完美）匹配。首先，我们证明了在二叉图上，这个问题是多项式时间可解的；其次，我们证明了以 k 为参数的 Diverse Pair of Maximum Matchings 是 \(\textsf{FPT}\)的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Diverse Pairs of Matchings

We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse Pair of Matchings (asking for two not necessarily maximum or perfect matchings) is \(\textsf{NP}\)-complete on general graphs if k is part of the input, and we consider two restricted variants. First, we show that on bipartite graphs, the problem is polynomial-time solvable, and second we show that Diverse Pair of Maximum Matchings is \(\textsf{FPT}\) parameterized by k. We round off the work by showing that Diverse Pair of Matchings has a kernel on \({\mathcal {O}}(k^2)\) vertices.

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

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.

期刊最新文献

Energy Constrained Depth First Search Recovering the Original Simplicity: Succinct and Exact Quantum Algorithm for the Welded Tree Problem Permutation-constrained Common String Partitions with Applications Reachability of Fair Allocations via Sequential Exchanges On Flipping the Fréchet Distance