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Cutting Polygons into Small Pieces with Chords: Laser-Based Localization
arXiv - CS - Discrete Mathematics Pub Date : 2020-06-26 , DOI: arxiv-2006.15089
Esther M. Arkin, Rathish Das, Jie Gao, Mayank Goswami, Joseph S. B. Mitchell, Valentin Polishchuk, Csaba D. Toth

Motivated by indoor localization by tripwire lasers, we study the problem of cutting a polygon into small-size pieces, using the chords of the polygon. Several versions are considered, depending on the definition of the "size" of a piece. In particular, we consider the area, the diameter, and the radius of the largest inscribed circle as a measure of the size of a piece. We also consider different objectives, either minimizing the maximum size of a piece for a given number of chords, or minimizing the number of chords that achieve a given size threshold for the pieces. We give hardness results for polygons with holes and approximation algorithms for multiple variants of the problem.

中文翻译:

用弦将多边形切割成小块:基于激光的定位

受绊线激光器室内定位的启发,我们研究了使用多边形的弦将多边形切割成小尺寸块的问题。考虑了几个版本,这取决于一块“大小”的定义。特别是,我们将最大内切圆的面积、直径和半径视为衡量一块大小的尺度。我们还考虑了不同的目标,要么最小化给定数量和弦的最大尺寸,要么最小化达到给定尺寸阈值的和弦数量。我们给出了带孔多边形的硬度结果和问题的多种变体的近似算法。
更新日期:2020-06-29
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