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.STACS.2020.13
URN: urn:nbn:de:0030-drops-118741
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11874/
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Bergren, Dan ; Eiben, Eduard ; Ganian, Robert ; Kanj, Iyad

On Covering Segments with Unit Intervals

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LIPIcs-STACS-2020-13.pdf (0.6 MB)

Abstract

We study the problem of covering a set of segments on a line with the minimum number of unit-length intervals, where an interval covers a segment if at least one of the two endpoints of the segment falls in the unit interval. We also study several variants of this problem.
We show that the restrictions of the aforementioned problems to the set of instances in which all the segments have the same length are NP-hard. This result implies several NP-hardness results in the literature for variants and generalizations of the problems under consideration.
We then study the parameterized complexity of the aforementioned problems. We provide tight results for most of them by showing that they are fixed-parameter tractable for the restrictions in which all the segments have the same length, and are W[1]-complete otherwise.

BibTeX - Entry

@InProceedings{bergren_et_al:LIPIcs:2020:11874,
  author =	{Dan Bergren and Eduard Eiben and Robert Ganian and Iyad Kanj},
  title =	{{On Covering Segments with Unit Intervals}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11874},
  URN =		{urn:nbn:de:0030-drops-118741},
  doi =		{10.4230/LIPIcs.STACS.2020.13},
  annote =	{Keywords: Segment covering, unit intervals, NP-completeness, parameterized complexity}
}

Keywords: Segment covering, unit intervals, NP-completeness, parameterized complexity
Collection: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue Date: 2020
Date of publication: 04.03.2020

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