Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

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.
Document type :
Conference papers
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01518713
Contributor : Aline Parreau <>
Submitted on : Friday, May 5, 2017 - 11:33:07 AM
Last modification on : Wednesday, April 3, 2019 - 1:08:47 AM
Long-term archiving on : Sunday, August 6, 2017 - 12:27:10 PM

Files

MDLDalgo_final.pdf
Files produced by the author(s)

Identifiers

Citation

Florent Foucaud, George Mertzios, Reza Naserasr, Aline Parreau, Petru Valicov. Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs. International Workshop on Graph-Theoretic Concepts in Computer Science WG 2015, Jun 2015, Munich, Germany. pp.175 - 471, ⟨10.1007/978-3-662-53174-7_32⟩. ⟨hal-01518713⟩

Share

Metrics

Record views

1383

Files downloads

315