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.APPROX-RANDOM.2019.32
URN: urn:nbn:de:0030-drops-112471
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11247/
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Huang, Chien-Chung ; Mari, Mathieu ; Mathieu, Claire ; Mitchell, Joseph S. B. ; Mustafa, Nabil H.

Maximizing Covered Area in the Euclidean Plane with Connectivity Constraint

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LIPIcs-APPROX-RANDOM-2019-32.pdf (2 MB)

Abstract

Given a set D of n unit disks in the plane and an integer k <= n, the maximum area connected subset problem asks for a set D' subseteq D of size k that maximizes the area of the union of disks, under the constraint that this union is connected. This problem is motivated by wireless router deployment and is a special case of maximizing a submodular function under a connectivity constraint.
We prove that the problem is NP-hard and analyze a greedy algorithm, proving that it is a 1/2-approximation. We then give a polynomial-time approximation scheme (PTAS) for this problem with resource augmentation, i.e., allowing an additional set of epsilon k disks that are not drawn from the input. Additionally, for two special cases of the problem we design a PTAS without resource augmentation.

BibTeX - Entry

@InProceedings{huang_et_al:LIPIcs:2019:11247,
  author =	{Chien-Chung Huang and Mathieu Mari and Claire Mathieu and Joseph S. B. Mitchell and Nabil H. Mustafa},
  title =	{{Maximizing Covered Area in the Euclidean Plane with Connectivity Constraint}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11247},
  URN =		{urn:nbn:de:0030-drops-112471},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.32},
  annote =	{Keywords: approximation algorithm, submodular function optimisation, unit disk graph, connectivity constraint}
}

Keywords: approximation algorithm, submodular function optimisation, unit disk graph, connectivity constraint
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Issue Date: 2019
Date of publication: 17.09.2019

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