在Voronoi可视地图1.5D地形与多视点

V. Keikha, Maria Saumell
{"title":"在Voronoi可视地图1.5D地形与多视点","authors":"V. Keikha, Maria Saumell","doi":"10.48550/arXiv.2301.05049","DOIUrl":null,"url":null,"abstract":"Given an $n$-vertex 1.5D terrain $\\T$ and a set $\\A$ of $m<n$ viewpoints, the Voronoi visibility map $\\vorvis(\\T,\\A)$ is a partitioning of $\\T$ into regions such that each region is assigned to the closest (in Euclidean distance) visible viewpoint. The colored visibility map $\\colvis(\\T,\\A)$ is a partitioning of $\\T$ into regions that have the same set of visible viewpoints. In this paper, we propose an algorithm to compute $\\vorvis(\\T,\\A)$ that runs in $O(n+(m^2+k_c)\\log n)$ time, where $k_c$ and $k_v$ denote the total complexity of $\\colvis(\\T,\\A)$ and $\\vorvis(\\T,\\A)$, respectively. This improves upon a previous algorithm for this problem. We also generalize our algorithm to higher order Voronoi visibility maps, and to Voronoi visibility maps with respect to other distances. Finally, we prove bounds relating $k_v$ to $k_c$, and we show an application of our algorithm to a problem on limited range of sight.","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Voronoi visibility maps of 1.5D terrains with multiple viewpoints\",\"authors\":\"V. Keikha, Maria Saumell\",\"doi\":\"10.48550/arXiv.2301.05049\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given an $n$-vertex 1.5D terrain $\\\\T$ and a set $\\\\A$ of $m<n$ viewpoints, the Voronoi visibility map $\\\\vorvis(\\\\T,\\\\A)$ is a partitioning of $\\\\T$ into regions such that each region is assigned to the closest (in Euclidean distance) visible viewpoint. The colored visibility map $\\\\colvis(\\\\T,\\\\A)$ is a partitioning of $\\\\T$ into regions that have the same set of visible viewpoints. In this paper, we propose an algorithm to compute $\\\\vorvis(\\\\T,\\\\A)$ that runs in $O(n+(m^2+k_c)\\\\log n)$ time, where $k_c$ and $k_v$ denote the total complexity of $\\\\colvis(\\\\T,\\\\A)$ and $\\\\vorvis(\\\\T,\\\\A)$, respectively. This improves upon a previous algorithm for this problem. We also generalize our algorithm to higher order Voronoi visibility maps, and to Voronoi visibility maps with respect to other distances. Finally, we prove bounds relating $k_v$ to $k_c$, and we show an application of our algorithm to a problem on limited range of sight.\",\"PeriodicalId\":13545,\"journal\":{\"name\":\"Inf. Process. Lett.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Inf. Process. Lett.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2301.05049\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inf. Process. Lett.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2301.05049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

给定一个$n$顶点的1.5D地形$\T$和$m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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
On Voronoi visibility maps of 1.5D terrains with multiple viewpoints
Given an $n$-vertex 1.5D terrain $\T$ and a set $\A$ of $m
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
自引率
0.00%
发文量
0
期刊最新文献
Monochromatic partitioning of colored points by lines An Improved Kernel for the Flip Distance Problem on Simple Convex Polygons Improved Bounds for Rectangular Monotone Min-Plus Product On Voronoi visibility maps of 1.5D terrains with multiple viewpoints Polynomial recognition of vulnerable multi-commodities
×
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
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1