最小凸面覆盖和最大隐集概述

arXiv - CS - Computational Geometry Pub Date : 2024-03-03 DOI:arxiv-2403.01354

Reilly Browne

{"title":"最小凸面覆盖和最大隐集概述","authors":"Reilly Browne","doi":"arxiv-2403.01354","DOIUrl":null,"url":null,"abstract":"We give a review of results on the minimum convex cover and maximum hidden\nset problems. In addition, we give some new results. First we show that it is\nNP-hard to determine whether a polygon has the same convex cover number as its\nhidden set number. We then give some important examples in which these\nquantities don't always coincide. Finally, We present some consequences of\ninsights from Browne, Kasthurirangan, Mitchell and Polishchuk [FOCS, 2023] on\nother classes of simple polygons.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Overview of Minimum Convex Cover and Maximum Hidden Set\",\"authors\":\"Reilly Browne\",\"doi\":\"arxiv-2403.01354\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a review of results on the minimum convex cover and maximum hidden\\nset problems. In addition, we give some new results. First we show that it is\\nNP-hard to determine whether a polygon has the same convex cover number as its\\nhidden set number. We then give some important examples in which these\\nquantities don't always coincide. Finally, We present some consequences of\\ninsights from Browne, Kasthurirangan, Mitchell and Polishchuk [FOCS, 2023] on\\nother classes of simple polygons.\",\"PeriodicalId\":501570,\"journal\":{\"name\":\"arXiv - CS - Computational Geometry\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-03\",\"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-2403.01354\",\"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-2403.01354","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

我们回顾了有关最小凸盖和最大隐集问题的结果。此外，我们还给出了一些新结果。首先，我们证明了要确定一个多边形是否具有与其隐藏集数相同的凸面覆盖数是NP难的。然后，我们给出了一些重要的例子，在这些例子中，这些数量并不总是重合的。最后，我们介绍了 Browne、Kasthurirangan、Mitchell 和 Polishchuk [FOCS, 2023] 对其他类简单多边形的见解的一些后果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An Overview of Minimum Convex Cover and Maximum Hidden Set

We give a review of results on the minimum convex cover and maximum hidden set problems. In addition, we give some new results. First we show that it is NP-hard to determine whether a polygon has the same convex cover number as its hidden set number. We then give some important examples in which these quantities don't always coincide. Finally, We present some consequences of insights from Browne, Kasthurirangan, Mitchell and Polishchuk [FOCS, 2023] on other classes of simple polygons.

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