Identification, location-domination and metric dimension on interval and permutation graphs. II. Algorithms and complexity

Abstract : We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted Identifying Code, (Open) Open Locating-Dominating Set and Metric Dimension) of an interval or a permutation graph. In these problems, one asks to distinguish all vertices of a graph by a subset of the vertices, using either the neighbourhood within the solution set or the distances to the solution vertices. Using a general reduction for this class of problems, we prove that the decision problems associated to these four notions are NP-complete, even for interval graphs of diameter 2 and permutation graphs of diameter 2. While Identifying Code and (Open) Locating-Dominating Set are trivially fixed-parameter-tractable when parameterized by solution size, it is known that in the same setting 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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https://hal.archives-ouvertes.fr/hal-01198784
Contributor : Petru Valicov <>
Submitted on : Monday, September 14, 2015 - 1:44:21 PM
Last modification on : Wednesday, November 20, 2019 - 2:32:02 AM

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Florent Foucaud, George B. Mertzios, Reza Naserasr, Aline Parreau, Petru Valicov. Identification, location-domination and metric dimension on interval and permutation graphs. II. Algorithms and complexity. Algorithmica, Springer Verlag, 2016, 78 (3), pp.914-944. ⟨10.1007/s00453-016-0184-1⟩. ⟨hal-01198784⟩

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