欧几里得最小权值拉曼图的有效算法及边相交性质

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
Yuya Higashikawa, N. Katoh, Yuki Kobayashi
{"title":"欧几里得最小权值拉曼图的有效算法及边相交性质","authors":"Yuya Higashikawa, N. Katoh, Yuki Kobayashi","doi":"10.1080/23799927.2023.2184723","DOIUrl":null,"url":null,"abstract":"We investigate the Euclidean minimum weight Laman graph on a planar point set P, for short. Bereg et al. (2016) studied geometric properties of and showed that the upper and lower bounds for the total number of edge crossings in are and , respectively. In this paper, we improve these upper and lower bounds to and for any , respectively. For improving the upper bound, we introduce a novel counting scheme based on some geometric observations. We also propose an time algorithm for computing , which was regarded as one of interesting future works by Bereg et al. (2016).","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Efficient algorithms and edge crossing properties of Euclidean minimum weight Laman graphs\",\"authors\":\"Yuya Higashikawa, N. Katoh, Yuki Kobayashi\",\"doi\":\"10.1080/23799927.2023.2184723\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the Euclidean minimum weight Laman graph on a planar point set P, for short. Bereg et al. (2016) studied geometric properties of and showed that the upper and lower bounds for the total number of edge crossings in are and , respectively. In this paper, we improve these upper and lower bounds to and for any , respectively. For improving the upper bound, we introduce a novel counting scheme based on some geometric observations. We also propose an time algorithm for computing , which was regarded as one of interesting future works by Bereg et al. (2016).\",\"PeriodicalId\":37216,\"journal\":{\"name\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/23799927.2023.2184723\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computer Mathematics: Computer Systems Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/23799927.2023.2184723","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0

摘要

研究了平面点集P上的欧几里得最小权值拉曼图。Bereg et al.(2016)研究了的几何性质,并表明,边缘交叉总数的上限和下限分别为和。在本文中,我们分别改进了和的上界和下界。为了改进上界,我们引入了一种新的基于几何观察的计数方案。我们还提出了一种用于计算的时间算法,这被Bereg等人(2016)视为有趣的未来工作之一。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient algorithms and edge crossing properties of Euclidean minimum weight Laman graphs
We investigate the Euclidean minimum weight Laman graph on a planar point set P, for short. Bereg et al. (2016) studied geometric properties of and showed that the upper and lower bounds for the total number of edge crossings in are and , respectively. In this paper, we improve these upper and lower bounds to and for any , respectively. For improving the upper bound, we introduce a novel counting scheme based on some geometric observations. We also propose an time algorithm for computing , which was regarded as one of interesting future works by Bereg et al. (2016).
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
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信