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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2023.66
URN: urn:nbn:de:0030-drops-187195
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18719/
Jansen, Bart M. P. ;
de Kroon, Jari J. H. ;
Włodarczyk, Michał
5-Approximation for ℋ-Treewidth Essentially as Fast as ℋ-Deletion Parameterized by Solution Size
Abstract
The notion of ℋ-treewidth, where ℋ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of ℋ-treewidth at most k can be decomposed into (arbitrarily large) ℋ-subgraphs which interact only through vertex sets of size ?(k) which can be organized in a tree-like fashion. ℋ-treewidth can be used as a hybrid parameterization to develop fixed-parameter tractable algorithms for ℋ-deletion problems, which ask to find a minimum vertex set whose removal from a given graph G turns it into a member of ℋ. The bottleneck in the current parameterized algorithms lies in the computation of suitable tree ℋ-decompositions.
We present FPT-approximation algorithms to compute tree ℋ-decompositions for hereditary and union-closed graph classes ℋ. Given a graph of ℋ-treewidth k, we can compute a 5-approximate tree ℋ-decomposition in time f(?(k)) ⋅ n^?(1) whenever ℋ-deletion parameterized by solution size can be solved in time f(k) ⋅ n^?(1) for some function f(k) ≥ 2^k. The current-best algorithms either achieve an approximation factor of k^?(1) or construct optimal decompositions while suffering from non-uniformity with unknown parameter dependence. Using these decompositions, we obtain algorithms solving Odd Cycle Transversal in time 2^?(k) ⋅ n^?(1) parameterized by bipartite-treewidth and Vertex Planarization in time 2^?(k log k) ⋅ n^?(1) parameterized by planar-treewidth, showing that these can be as fast as the solution-size parameterizations and giving the first ETH-tight algorithms for parameterizations by hybrid width measures.
BibTeX - Entry
@InProceedings{jansen_et_al:LIPIcs.ESA.2023.66,
author = {Jansen, Bart M. P. and de Kroon, Jari J. H. and W{\l}odarczyk, Micha{\l}},
title = {{5-Approximation for ℋ-Treewidth Essentially as Fast as ℋ-Deletion Parameterized by Solution Size}},
booktitle = {31st Annual European Symposium on Algorithms (ESA 2023)},
pages = {66:1--66:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-295-2},
ISSN = {1868-8969},
year = {2023},
volume = {274},
editor = {G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18719},
URN = {urn:nbn:de:0030-drops-187195},
doi = {10.4230/LIPIcs.ESA.2023.66},
annote = {Keywords: fixed-parameter tractability, treewidth, graph decompositions}
}
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Keywords: |
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fixed-parameter tractability, treewidth, graph decompositions |
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Collection: |
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31st Annual European Symposium on Algorithms (ESA 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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30.08.2023 |
