Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Computer Science

Profile

Publication details for Dr George Mertzios

Foucaud, F., Mertzios, G.B., Naserasr, R., Parreau, A. & Valicov, P. (2016), Algorithms and complexity for metric dimension and location-domination on interval and permutation graphs, in Mayr, Ernst W. eds, Lecture notes in computer science, 9224 41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG). Munich, Germany, Springer, Berlin, 456-471.

Author(s) from Durham

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.