License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2021.24
URN: urn:nbn:de:0030-drops-154071
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15407/
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Li, Shaohua ; Pilipczuk, Marcin

Hardness of Metric Dimension in Graphs of Constant Treewidth

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LIPIcs-IPEC-2021-24.pdf (1 MB)


Abstract

The Metric Dimension problem asks for a minimum-sized resolving set in a given (unweighted, undirected) graph G. Here, a set S ⊆ V(G) is resolving if no two distinct vertices of G have the same distance vector to S. 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.

BibTeX - Entry

@InProceedings{li_et_al:LIPIcs.IPEC.2021.24,
  author =	{Li, Shaohua and Pilipczuk, Marcin},
  title =	{{Hardness of Metric Dimension in Graphs of Constant Treewidth}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15407},
  URN =		{urn:nbn:de:0030-drops-154071},
  doi =		{10.4230/LIPIcs.IPEC.2021.24},
  annote =	{Keywords: Graph algorithms, parameterized complexity, width parameters, NP-hard}
}

Keywords: Graph algorithms, parameterized complexity, width parameters, NP-hard
Collection: 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)
Issue Date: 2021
Date of publication: 22.11.2021


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