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.ISAAC.2018.52
URN: urn:nbn:de:0030-drops-100003
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10000/
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Keikha, Vahideh ; van de Kerkhof, Mees ; van Kreveld, Marc ; Kostitsyna, Irina ; Löffler, Maarten ; Staals, Frank ; Urhausen, Jérôme ; Vermeulen, Jordi L. ; Wiratma, Lionov

Convex Partial Transversals of Planar Regions

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LIPIcs-ISAAC-2018-52.pdf (0.6 MB)

Abstract

We consider the problem of testing, for a given set of planar regions R and an integer k, whether there exists a convex shape whose boundary intersects at least k regions of R. We provide polynomial-time algorithms for the case where the regions are disjoint axis-aligned rectangles or disjoint line segments with a constant number of orientations. On the other hand, we show that the problem is NP-hard when the regions are intersecting axis-aligned rectangles or 3-oriented line segments. For several natural intermediate classes of shapes (arbitrary disjoint segments, intersecting 2-oriented segments) the problem remains open.

BibTeX - Entry

@InProceedings{keikha_et_al:LIPIcs:2018:10000,
  author =	{Vahideh Keikha and Mees van de Kerkhof and Marc van Kreveld and Irina Kostitsyna and Maarten L{\"o}ffler and Frank Staals and J{\'e}r{\^o}me Urhausen and Jordi L. Vermeulen and Lionov Wiratma},
  title =	{{Convex Partial Transversals of Planar Regions}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{52:1--52:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10000},
  URN =		{urn:nbn:de:0030-drops-100003},
  doi =		{10.4230/LIPIcs.ISAAC.2018.52},
  annote =	{Keywords: computational geometry, algorithms, NP-hardness, convex transversals}
}

Keywords: computational geometry, algorithms, NP-hardness, convex transversals
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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