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

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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。

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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.

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arXiv - CS - Computational Geometry

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