发布求助
文献互助 智能选刊 最新文献

Drawing graphs in the plane with high resolution

Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science Pub Date : 1990-10-22 DOI:10.1109/FSCS.1990.89527
Michael Formann, T. Hagerup, J. Haralambides, Michael Kaufmann, F. Leighton, A. Symvonis, E. Welzl, G. Woeginger
{"title":"Drawing graphs in the plane with high resolution","authors":"Michael Formann, T. Hagerup, J. Haralambides, Michael Kaufmann, F. Leighton, A. Symvonis, E. Welzl, G. Woeginger","doi":"10.1109/FSCS.1990.89527","DOIUrl":null,"url":null,"abstract":"The problem of drawing a graph in the plane so that edges appear as straight lines and the minimum angle formed by any pair of incident edges is maximized is studied. The resolution of a layout is defined to be the size of the minimum angle formed by incident edges of the graph, and the resolution of a graph is defined to be the maximum resolution of any layout of the graph. The resolution R of a graph is characterized in terms of the maximum node degree d of the graph by proving that Omega (1/d/sup 2/)<or=R<or=2 pi /d for any graph. Moreover, it is proved that R= Theta (1/d) for many graphs, including planar graphs, complete graphs, hypercubes, multidimensional meshes and tori, and other special networks. It is also shown that the problem of deciding if R=2 pi /d for a graph is NP-hard for d=4, and a counting argument is used to show that R=O(log d/d/sup 2/) for many graphs.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FSCS.1990.89527","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 24

Abstract

The problem of drawing a graph in the plane so that edges appear as straight lines and the minimum angle formed by any pair of incident edges is maximized is studied. The resolution of a layout is defined to be the size of the minimum angle formed by incident edges of the graph, and the resolution of a graph is defined to be the maximum resolution of any layout of the graph. The resolution R of a graph is characterized in terms of the maximum node degree d of the graph by proving that Omega (1/d/sup 2/)>
分享
查看原文 本刊更多论文
在平面上绘制高分辨率的图形
研究了平面上的图的绘制问题，使任意一对入射边形成的最小夹角最大，并使边呈直线状。布局的分辨率定义为图的入射边形成的最小角度的大小，图的分辨率定义为图的任何布局的最大分辨率。通过证明ω (1/d/sup 2/)>，用图的最大节点度d来表征图的分辨率R
本文章由计算机程序翻译，如有差异，请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science
Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science
自引率
0.00%
发文量
0
×
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
现在去查看 取消
×
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