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.2022.8
URN: urn:nbn:de:0030-drops-173640
URL: https://drops.dagstuhl.de/opus/volltexte/2022/17364/
Bodlaender, Hans L. ;
Groenland, Carla ;
Jacob, Hugo ;
Jaffke, Lars ;
Lima, Paloma T.
XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure
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.
BibTeX - Entry
@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2022.8,
author = {Bodlaender, Hans L. and Groenland, Carla and Jacob, Hugo and Jaffke, Lars and Lima, Paloma T.},
title = {{XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure}},
booktitle = {17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
pages = {8:1--8:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-260-0},
ISSN = {1868-8969},
year = {2022},
volume = {249},
editor = {Dell, Holger and Nederlof, Jesper},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/17364},
URN = {urn:nbn:de:0030-drops-173640},
doi = {10.4230/LIPIcs.IPEC.2022.8},
annote = {Keywords: parameterized complexity, XNLP, linear clique-width, W-hierarchy, pathwidth, linear mim-width, bandwidth}
}
Keywords: |
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parameterized complexity, XNLP, linear clique-width, W-hierarchy, pathwidth, linear mim-width, bandwidth |
Collection: |
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17th International Symposium on Parameterized and Exact Computation (IPEC 2022) |
Issue Date: |
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2022 |
Date of publication: |
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14.12.2022 |