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 . Here, a set is resolving if no two distinct vertices of have the same distance vector to . 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.
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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}
}