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.ESA.2023.33
URN: urn:nbn:de:0030-drops-186865
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18686/
Chalermsook, Parinya ;
Fomin, Fedor ;
Hamm, Thekla ;
Korhonen, Tuukka ;
Nederlof, Jesper ;
Orgo, Ly
Polynomial-Time Approximation of Independent Set Parameterized by Treewidth
Abstract
We prove the following result about approximating the maximum independent set in a graph. Informally, we show that any approximation algorithm with a "non-trivial" approximation ratio (as a function of the number of vertices of the input graph G) can be turned into an approximation algorithm achieving almost the same ratio, albeit as a function of the treewidth of G. More formally, we prove that for any function f, the existence of a polynomial time (n/f(n))-approximation algorithm yields the existence of a polynomial time O(tw⋅log{f(tw)}/f(tw))-approximation algorithm, where n and tw denote the number of vertices and the width of a given tree decomposition of the input graph. By pipelining our result with the state-of-the-art O(n ⋅ (log log n)²/log³n)-approximation algorithm by Feige (2004), this implies an O(tw⋅(log log tw)³/log³tw)-approximation algorithm.
BibTeX - Entry
@InProceedings{chalermsook_et_al:LIPIcs.ESA.2023.33,
author = {Chalermsook, Parinya and Fomin, Fedor and Hamm, Thekla and Korhonen, Tuukka and Nederlof, Jesper and Orgo, Ly},
title = {{Polynomial-Time Approximation of Independent Set Parameterized by Treewidth}},
booktitle = {31st Annual European Symposium on Algorithms (ESA 2023)},
pages = {33:1--33:13},
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/2023/18686},
URN = {urn:nbn:de:0030-drops-186865},
doi = {10.4230/LIPIcs.ESA.2023.33},
annote = {Keywords: Maximum Independent Set, Treewidth, Approximation Algorithms, Parameterized Approximation}
}
Keywords: |
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Maximum Independent Set, Treewidth, Approximation Algorithms, Parameterized Approximation |
Collection: |
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31st Annual European Symposium on Algorithms (ESA 2023) |
Issue Date: |
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2023 |
Date of publication: |
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30.08.2023 |