Publication details for Dr George MertziosFoucaud, 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.
- Publication type: Journal Article
- ISSN/ISBN: 0178-4617, 1432-0541
- DOI: 10.1007/s00453-016-0184-1
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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-hard. We show that for interval graphs, this parameterization of Metric Dimension is fixed-parameter-tractable.