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Algorithms and complexity for metric dimension and location-domination on interval and permutation graphs.

Foucaud, F. and Mertzios, G.B. and Naserasr, R. and Parreau, A. and Valicov, P. (2016) 'Algorithms and complexity for metric dimension and location-domination on interval and permutation graphs.', in Graph-theoretic concepts in computer science : 41st international workshop, WG 2015, Garching, Germany, June 17-19, 2015 ; revised papers. Berlin: Springer, pp. 456-471. Lecture notes in computer science. (9224).


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.

Item Type:Book chapter
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Date accepted:28 April 2015
Date deposited:03 August 2015
Date of first online publication:05 August 2016
Date first made open access:05 August 2017

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