Brief Announcement: Approximation Schemes for Geometric Coverage Problems

Authors Steven Chaplick , Minati De, Alexander Ravsky, Joachim Spoerhase

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Author Details

Steven Chaplick
  • Lehrstuhl für Informatik I, Universität Würzburg, Germany
Minati De
  • Department of Mathematics, Indian Institute of Technology Delhi, India
Alexander Ravsky
  • Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Science of Ukraine, Lviv, Ukraine
Joachim Spoerhase
  • Lehrstuhl für Informatik I, Universität Würzburg, Germany
  • , Institute of Computer Science, University of Wrocław, Poland.

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Steven Chaplick, Minati De, Alexander Ravsky, and Joachim Spoerhase. Brief Announcement: Approximation Schemes for Geometric Coverage Problems. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 107:1-107:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • balanced separators
  • maximum coverage
  • local search
  • approximation scheme
  • geometric approximation algorithms


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