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Durham University

Computer Science

Profile

Publication details for Dr George Mertzios

Foucaud, F., Mertzios, G.B., Naserasr, R., Parreau, A. & Valicov, P. (2017). Identification, location-domination and metric dimension on interval and permutation graphs. II. Algorithms and complexity. Algorithmica 78(3): 914-944.

Author(s) from Durham

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.