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Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

  • Florent Foucaud
  • George B. Mertzios
  • Reza Naserasr
  • Aline ParreauEmail author
  • Petru Valicov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

We study the problems Locating-Dominating Set and Metric Dimension, which consist of determining a minimum-size set of vertices that distinguishes the vertices of a graph using either neighbourhoods or distances. We consider these problems when restricted to interval graphs and permutation graphs. We prove that both decision problems are NP-complete, even for graphs that are at the same time interval graphs and permutation graphs and have diameter 2. While Locating-Dominating Set parameterized by solution size is trivially fixed-parameter-tractable, it is known that Metric Dimension is W[2]-hard. We show that for interval graphs, this parameterization of Metric Dimension is fixed-parameter-tractable.

Notes

Acknowledgments

We thank Adrian Kosowski for helpful discussions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Florent Foucaud
    • 1
  • George B. Mertzios
    • 2
  • Reza Naserasr
    • 3
  • Aline Parreau
    • 4
    Email author
  • Petru Valicov
    • 5
  1. 1.Université Blaise Pascal, LIMOS - CNRS UMR 6158Clermont-FerrandFrance
  2. 2.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  3. 3.CNRS - IRIF, Université Paris DiderotParisFrance
  4. 4.CNRS, LIRIS, UMR 5205, Université de LyonVilleurbanneFrance
  5. 5.CNRS, LIF, UMR 7279, Université d’Aix-MarseilleMarseilleFrance

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