The dominating set problem in geometric intersection graphs

Mark De Berg, Sándor Kisfaludi-Bak, Gerhard Woeginger

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Abstract

We study the parameterized complexity of dominating sets in geometric intersection graphs. • In one dimension, we investigate intersection graphs induced by translates of a fixed pattern Q that consists of a finite number of intervals and a finite number of isolated points. We prove that Dominating Set on such intersection graphs is polynomially solvable whenever Q contains at least one interval, and whenever Q contains no intervals and for any two point pairs in Q the distance ratio is rational. The remaining case where Q contains no intervals but does contain an irrational distance ratio is shown to be NP-complete and contained in FPT (when parameterized by the solution size). • In two and higher dimensions, we prove that Dominating Set is contained in W[1] for intersection graphs of semi-algebraic sets with constant description complexity. This generalizes known results from the literature. Finally, we establish W[1]-hardness for a large class of intersection graphs.

Original languageEnglish
Title of host publication12th International Symposium on Parameterized and Exact Computation, IPEC 2017
Place of PublicationDagstuhl
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Pages14:1-14:12
ISBN (Print)978-3-95977-051-4
DOIs
Publication statusPublished - 1 Feb 2018
Event12th International Symposium on Parameterized and Exact Computation (IPEC 2017) - Vienna, Austria
Duration: 6 Sep 20178 Sep 2017
Conference number: 12
https://algo2017.ac.tuwien.ac.at/ipec

Publication series

NameLIPIcs
Volume89

Conference

Conference12th International Symposium on Parameterized and Exact Computation (IPEC 2017)
Abbreviated titleIPEC 2017
CountryAustria
CityVienna
Period6/09/178/09/17
Internet address

Keywords

  • Dominating set
  • Intersection graph
  • W-hierarchy

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  • Cite this

    De Berg, M., Kisfaludi-Bak, S., & Woeginger, G. (2018). The dominating set problem in geometric intersection graphs. In 12th International Symposium on Parameterized and Exact Computation, IPEC 2017 (pp. 14:1-14:12). (LIPIcs; Vol. 89). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.IPEC.2017.14