稳健地保护多边形

arXiv - CS - Computational Geometry Pub Date : 2024-03-18 DOI:arxiv-2403.11861

Rathish Das, Omrit Filtser, Matthew J. Katz, Joseph S. B. Mitchell

{"title":"稳健地保护多边形","authors":"Rathish Das, Omrit Filtser, Matthew J. Katz, Joseph S. B. Mitchell","doi":"arxiv-2403.11861","DOIUrl":null,"url":null,"abstract":"We propose precise notions of what it means to guard a domain \"robustly\",\nunder a variety of models. While approximation algorithms for minimizing the\nnumber of (precise) point guards in a polygon is a notoriously challenging area\nof investigation, we show that imposing various degrees of robustness on the\nnotion of visibility coverage leads to a more tractable (and realistic) problem\nfor which we can provide approximation algorithms with constant factor\nguarantees.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Robustly Guarding Polygons\",\"authors\":\"Rathish Das, Omrit Filtser, Matthew J. Katz, Joseph S. B. Mitchell\",\"doi\":\"arxiv-2403.11861\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose precise notions of what it means to guard a domain \\\"robustly\\\",\\nunder a variety of models. While approximation algorithms for minimizing the\\nnumber of (precise) point guards in a polygon is a notoriously challenging area\\nof investigation, we show that imposing various degrees of robustness on the\\nnotion of visibility coverage leads to a more tractable (and realistic) problem\\nfor which we can provide approximation algorithms with constant factor\\nguarantees.\",\"PeriodicalId\":501570,\"journal\":{\"name\":\"arXiv - CS - Computational Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Computational Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2403.11861\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.11861","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

我们提出了在各种模型下 "稳健地 "保护一个域的精确概念。虽然最小化多边形中（精确）点防护数量的近似算法是一个众所周知的具有挑战性的研究领域，但我们表明，对可见度覆盖范围的运动施加不同程度的鲁棒性，会带来一个更容易解决（也更现实）的问题，我们可以为其提供具有恒定系数保证的近似算法。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Robustly Guarding Polygons

We propose precise notions of what it means to guard a domain "robustly", under a variety of models. While approximation algorithms for minimizing the number of (precise) point guards in a polygon is a notoriously challenging area of investigation, we show that imposing various degrees of robustness on the notion of visibility coverage leads to a more tractable (and realistic) problem for which we can provide approximation algorithms with constant factor guarantees.

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

arXiv - CS - Computational Geometry

自引率

0.00%

发文量

期刊最新文献

Minimum Plane Bichromatic Spanning Trees Evolving Distributions Under Local Motion New Lower Bound and Algorithms for Online Geometric Hitting Set Problem Computing shortest paths amid non-overlapping weighted disks Fast Comparative Analysis of Merge Trees Using Locality Sensitive Hashing