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DOI: 10.4230/LIPIcs.ESA.2020.7
URN: urn:nbn:de:0030-drops-128736
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12873/
Arkin, Esther M. ; Das, Rathish ; Gao, Jie ; Goswami, Mayank ; Mitchell, Joseph S. B. ; Polishchuk, Valentin ; Tóth, Csaba D.
Cutting Polygons into Small Pieces with Chords: Laser-Based Localization
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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.
BibTeX - Entry
@InProceedings{arkin_et_al:LIPIcs:2020:12873,
author = {Esther M. Arkin and Rathish Das and Jie Gao and Mayank Goswami and Joseph S. B. Mitchell and Valentin Polishchuk and Csaba D. T{\'o}th},
title = {{Cutting Polygons into Small Pieces with Chords: Laser-Based Localization}},
booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)},
pages = {7:1--7:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-162-7},
ISSN = {1868-8969},
year = {2020},
volume = {173},
editor = {Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12873},
URN = {urn:nbn:de:0030-drops-128736},
doi = {10.4230/LIPIcs.ESA.2020.7},
annote = {Keywords: Polygon partition, Arrangements, Visibility, Localization}
}
| Keywords: | Polygon partition, Arrangements, Visibility, Localization | |
| Seminar: | 28th Annual European Symposium on Algorithms (ESA 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 26.08.2020 |
