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

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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。

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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.

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arXiv - CS - Computational Geometry

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