Hardness of Metric Dimension in Graphs of Constant Treewidth

Authors Shaohua Li , Marcin Pilipczuk

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Shaohua Li
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
Marcin Pilipczuk
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland

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Shaohua Li and Marcin Pilipczuk. Hardness of Metric Dimension in Graphs of Constant Treewidth. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Graph algorithms
  • parameterized complexity
  • width parameters
  • NP-hard


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