Cutting Polygons into Small Pieces with Chords: Laser-Based Localization
Computational Geometry
2020-06-29 v1 Discrete Mathematics
Data Structures and Algorithms
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.
Cite
@article{arxiv.2006.15089,
title = {Cutting Polygons into Small Pieces with Chords: Laser-Based Localization},
author = {Esther M. Arkin and Rathish Das and Jie Gao and Mayank Goswami and Joseph S. B. Mitchell and Valentin Polishchuk and Csaba D. Toth},
journal= {arXiv preprint arXiv:2006.15089},
year = {2020}
}
Comments
This paper will appear in ESA2020, Track A proceedings