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XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure

Authors Hans L. Bodlaender , Carla Groenland , Hugo Jacob , Lars Jaffke , Paloma T. Lima

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Author Details

Hans L. Bodlaender
  • Utrecht University, The Netherlands
Carla Groenland
  • Utrecht University, The Netherlands
Hugo Jacob
  • ENS Paris-Saclay, France
Lars Jaffke
  • University of Bergen, Norway
Paloma T. Lima
  • IT University of Copenhagen, Denmark

Funding

  • Groenland, Carla: Supported by the European Union’s Horizon 2020 research and innovation programme under the ERC grant CRACKNP (number 853234) and the Marie Skłodowska-Curie grant GRAPHCOSY (number 101063180).
  • Jaffke, Lars: Supported by the Norwegian Research Council (project number 274526) and the Meltzer Research Fund.

Cite As Get BibTex

Hans L. Bodlaender, Carla Groenland, Hugo Jacob, Lars Jaffke, and Paloma T. Lima. XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.IPEC.2022.8

Abstract

In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing W[1]-hardness proofs for these problems, since XNLP-hardness implies W[t]-hardness for all t. It also indicates, via a conjecture by Pilipczuk and Wrochna [ToCT 2018], that any XP algorithm for such problems is likely to require XP space. 
In particular, we show XNLP-completeness for natural problems parameterized by pathwidth, linear clique-width, and linear mim-width. The problems we consider are Independent Set, Dominating Set, Odd Cycle Transversal, (q-)Coloring, Max Cut, Maximum Regular Induced Subgraph, Feedback Vertex Set, Capacitated (Red-Blue) Dominating Set, and Bipartite Bandwidth.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • parameterized complexity
  • XNLP
  • linear clique-width
  • W-hierarchy
  • pathwidth
  • linear mim-width
  • bandwidth

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References

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