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Hardness of Metric Dimension in Graphs of Constant Treewidth

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Abstract

The Metric Dimension problem asks for a minimum-sized resolving set in a given (unweighted, undirected) graph G. Here, a set \(S \subseteq V(G)\) 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 \(24\).

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Shaohua Li & Marcin Pilipczuk

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  1. Shaohua Li
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  2. Marcin Pilipczuk
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Correspondence to Shaohua Li.

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The authors of this paper, Shaohua Li and Marcin Pilipczuk, certify that there is no actual or potential conflict of interest in relation to this article.

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This research is a part of projects that have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 714704. A preliminary version appeared at IPEC 2021

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Li, S., Pilipczuk, M. Hardness of Metric Dimension in Graphs of Constant Treewidth. Algorithmica 84, 3110–3155 (2022). https://doi.org/10.1007/s00453-022-01005-y

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