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：

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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。