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.2019.19
URN: urn:nbn:de:0030-drops-112344
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11234/
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Kumar, Neeraj ; Sintos, Stavros ; Suri, Subhash

The Maximum Exposure Problem

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LIPIcs-APPROX-RANDOM-2019-19.pdf (0.7 MB)

Abstract

Given a set of points P and axis-aligned rectangles R in the plane, a point p in P is called exposed if it lies outside all rectangles in R. In the max-exposure problem, given an integer parameter k, we want to delete k rectangles from R so as to maximize the number of exposed points. We show that the problem is NP-hard and assuming plausible complexity conjectures is also hard to approximate even when rectangles in R are translates of two fixed rectangles. However, if R only consists of translates of a single rectangle, we present a polynomial-time approximation scheme. For general rectangle range space, we present a simple O(k) bicriteria approximation algorithm; that is by deleting O(k^2) rectangles, we can expose at least Omega(1/k) of the optimal number of points.

BibTeX - Entry

@InProceedings{kumar_et_al:LIPIcs:2019:11234,
  author =	{Neeraj Kumar and Stavros Sintos and Subhash Suri},
  title =	{{The Maximum Exposure Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{19:1--19:20},
  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/2019/11234},
  URN =		{urn:nbn:de:0030-drops-112344},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.19},
  annote =	{Keywords: max-exposure, PTAS, densest k-subgraphs, geometric constraint removal, Network resilience}
}

Keywords: max-exposure, PTAS, densest k-subgraphs, geometric constraint removal, Network resilience
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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