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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2015: Graph-Theoretic Concepts in Computer Science pp 456–471Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This is a short version of the full paper [16] available on arXiv:1405.2424.

G. Mertzios—Partially supported by the EPSRC Grant EP/K022660/1.

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Notes

  1. 1.

    Note that the intervals \(I_T\) are not part of the final construction.

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Acknowledgments

We thank Adrian Kosowski for helpful discussions.

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Authors and Affiliations

  1. Université Blaise Pascal, LIMOS - CNRS UMR 6158, Clermont-Ferrand, France

    Florent Foucaud

  2. School of Engineering and Computing Sciences, Durham University, Durham, UK

    George B. Mertzios

  3. CNRS - IRIF, Université Paris Diderot, Paris, France

    Reza Naserasr

  4. CNRS, LIRIS, UMR 5205, Université de Lyon, Villeurbanne, France

    Aline Parreau

  5. CNRS, LIF, UMR 7279, Université d’Aix-Marseille, Marseille, France

    Petru Valicov

Authors
  1. Florent Foucaud
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  2. George B. Mertzios
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  3. Reza Naserasr
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  4. Aline Parreau
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  5. Petru Valicov
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Corresponding author

Correspondence to Aline Parreau .

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Editors and Affiliations

  1. TU München Institut für Informatik, Garching, Germany

    Ernst W. Mayr

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Foucaud, F., Mertzios, G.B., Naserasr, R., Parreau, A., Valicov, P. (2016). Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs. In: Mayr, E. (eds) Graph-Theoretic Concepts in Computer Science. WG 2015. Lecture Notes in Computer Science(), vol 9224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53174-7_32

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  • DOI: https://doi.org/10.1007/978-3-662-53174-7_32

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