English

Hardness of Metric Dimension in Graphs of Constant Treewidth

Data Structures and Algorithms 2021-02-22 v1 Discrete Mathematics

Abstract

The Metric Dimension problem asks for a minimum-sized resolving set in a given (unweighted, undirected) graph GG. Here, a set SV(G)S \subseteq V(G) is resolving if no two distinct vertices of GG have the same distance vector to SS. The complexity of Metric Dimension in graphs of bounded treewidth remained elusive in the past years. Recently, Bonnet and Purohit [IPEC 2019] showed that the problem is W[1]-hard under treewidth parameterization. In this work, we strengthen their lower bound to show that Metric Dimension is NP-hard in graphs of treewidth 24.

Keywords

Cite

@article{arxiv.2102.09791,
  title  = {Hardness of Metric Dimension in Graphs of Constant Treewidth},
  author = {Shaohua Li and Marcin Pilipczuk},
  journal= {arXiv preprint arXiv:2102.09791},
  year   = {2021}
}