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Communication Dans Un Congrès Année : 2016

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

Résumé

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.
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Dates et versions

hal-01518713 , version 1 (05-05-2017)

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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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