On Covering Segments with Unit Intervals. / Bergren, Dan; Eiben, Eduard; Ganian, Robert; Kanj, Iyad.

2020. 13:1-13:17 Paper presented at The 37th International Symposium on Theoretical Aspects of Computer Science, Montpellier, France.

Research output: Contribution to conferencePaper

Published

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.
Original languageEnglish
Pages13:1-13:17
Number of pages17
DOIs
Publication statusPublished - 27 Feb 2020
EventThe 37th International Symposium on Theoretical Aspects of Computer Science - Montpellier, France
Duration: 10 Mar 202013 Mar 2020
https://stacs2020.sciencesconf.org/

Conference

ConferenceThe 37th International Symposium on Theoretical Aspects of Computer Science
Abbreviated titleSTACS 2020
CountryFrance
CityMontpellier
Period10/03/2013/03/20
Internet address
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ID: 37234755