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.ICALP.2018.107
URN: urn:nbn:de:0030-drops-91113
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9111/
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Chaplick, Steven ; De, Minati ; Ravsky, Alexander ; Spoerhase, Joachim

Brief Announcement: Approximation Schemes for Geometric Coverage Problems

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Abstract

In this announcement, we show that the classical Maximum Coverage problem (MC) admits a PTAS via local search in essentially all cases where the corresponding instances of Set Cover (SC) admit a PTAS via the local search approach by Mustafa and Ray [Nabil H. Mustafa and Saurabh Ray, 2010]. As a corollary, we answer an open question by Badanidiyuru, Kleinberg, and Lee [Ashwinkumar Badanidiyuru et al., 2012] regarding half-spaces in R^3 thereby settling the existence of PTASs for essentially all natural cases of geometric MC problems. As an intermediate result, we show a color-balanced version of the classical planar subdivision theorem by Frederickson [Greg N. Frederickson, 1987]. We believe that some of our ideas may be useful for analyzing local search in other settings involving a hard cardinality constraint.

BibTeX - Entry

@InProceedings{chaplick_et_al:LIPIcs:2018:9111,
  author =	{Steven Chaplick and Minati De and Alexander Ravsky and Joachim Spoerhase},
  title =	{{Brief Announcement: Approximation Schemes for Geometric Coverage Problems}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{107:1--107:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9111},
  URN =		{urn:nbn:de:0030-drops-91113},
  doi =		{10.4230/LIPIcs.ICALP.2018.107},
  annote =	{Keywords: balanced separators, maximum coverage, local search, approximation scheme, geometric approximation algorithms}
}

Keywords: balanced separators, maximum coverage, local search, approximation scheme, geometric approximation algorithms
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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