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

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

Conference Paper (2022)

Author(s)

Hans L. Bodlaender (Universiteit Utrecht)

Carla Groenland (Universiteit Utrecht)

Hugo Jacob (ENS Paris-Saclay)

Lars Jaffke (University of Bergen)

Paloma T. Lima (University of Copenhagen)

Affiliation

External organisation

Bandwidth Parameterized complexity W-hierarchy Pathwidth XNLP Linear clique-width Linear mim-width

DOI related publication

https://doi.org/10.4230/LIPIcs.IPEC.2022.8 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:8eaf98de-ea02-46d2-93b4-f7a40fe249f9

More Info

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Publication Year

2022

Language

English

Affiliation

External organisation

Article number

8

Publisher

Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ISBN (electronic)

9783959772600

Event

17th International Symposium on Parameterized and Exact Computation, IPEC 2022 (2022-09-07 - 2022-09-09), Potsdam, Germany

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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.