License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.7
URN: urn:nbn:de:0030-drops-128736
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12873/
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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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LIPIcs-ESA-2020-7.pdf (0.9 MB)

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
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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