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arXiv · 2006.15089

Cutting Polygons into Small Pieces with Chords: Laser-Based Localization

Esther M. Arkin·Rathish Das·Jie Gao·Mayank Goswami·Joseph S. B. Mitchell·Valentin Polishchuk·Csaba D. Toth
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Abstract

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.

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Esther M. Arkin, Rathish Das, Jie Gao, Mayank Goswami, Joseph S. B. Mitchell, Valentin Polishchuk, Csaba D. Toth. 2020-06-26. Cutting Polygons into Small Pieces with Chords: Laser-Based Localization. https://arxiv.org/abs/2006.15089

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