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

Florent Foucaud 1 George Mertzios 2 Reza Naserasr 3 Aline Parreau 4, 5 Petru Valicov 6
1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
2 School of Engineering and Computing Sciences
3 LRI - Laboratoire de Recherche en Informatique
4 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
5 Département de Mathématiques [Liège]
6 LIF - Laboratoire d'informatique Fondamentale de Marseille
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.
Keywords : Metric dimension Identifying codes Interval graphs Complexity
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Conference papers
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EC-LYON | EC-MARSEILLE | INSMI | UMR8623 | INRIA | LIF | LIRIS | UNIV-AMU | SIGMA-CLERMONT | PRES_CLERMONT | LIMOS | INSA-LYON | UNIV-LYON1 | LRI-GALAC | CENTRALESUPELEC | LIS-LAB | INSA-GROUPE | UNIV-LYON2

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Florent Foucaud, George Mertzios, Reza Naserasr, Aline Parreau, Petru Valicov. Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs. International Workshop on Graph-Theoretic Concepts in Computer Science WG 2015, Jun 2015, Munich, Germany. pp.175 - 471, ⟨10.1007/978-3-662-53174-7_32⟩. ⟨hal-01518713⟩

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