Identification, location-domination and metric dimension on interval and permutation graphs. II. Algorithms and complexity - Archive ouverte HAL Access content directly
Journal Articles Algorithmica Year : 2017

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.

Dates and versions

hal-01198784 , version 1 (14-09-2015)

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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, 2017, 78 (3), pp.914-944. ⟨10.1007/s00453-016-0184-1⟩. ⟨hal-01198784⟩
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