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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.93
URN: urn:nbn:de:0030-drops-164343
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16434/
Majewski, Konrad ;
Masařík, Tomáš ;
Novotná, Jana ;
Okrasa, Karolina ;
Pilipczuk, Marcin ;
Rzążewski, Paweł ;
Sokołowski, Marek
Max Weight Independent Set in Graphs with No Long Claws: An Analog of the Gyárfás' Path Argument
Abstract
We revisit recent developments for the Maximum Weight Independent Set problem in graphs excluding a subdivided claw S_{t,t,t} as an induced subgraph [Chudnovsky, Pilipczuk, Pilipczuk, Thomassé, SODA 2020] and provide a subexponential-time algorithm with improved running time 2^?(√nlog n) and a quasipolynomial-time approximation scheme with improved running time 2^?(ε^{-1} log⁵ n).
The Gyárfás' path argument, a powerful tool that is the main building block for many algorithms in P_t-free graphs, ensures that given an n-vertex P_t-free graph, in polynomial time we can find a set P of at most t-1 vertices, such that every connected component of G-N[P] has at most n/2 vertices. Our main technical contribution is an analog of this result for S_{t,t,t}-free graphs: given an n-vertex S_{t,t,t}-free graph, in polynomial time we can find a set P of ?(t log n) vertices and an extended strip decomposition (an appropriate analog of the decomposition into connected components) of G-N[P] such that every particle (an appropriate analog of a connected component to recurse on) of the said extended strip decomposition has at most n/2 vertices.
BibTeX - Entry
@InProceedings{majewski_et_al:LIPIcs.ICALP.2022.93,
author = {Majewski, Konrad and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Novotn\'{a}, Jana and Okrasa, Karolina and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l} and Soko{\l}owski, Marek},
title = {{Max Weight Independent Set in Graphs with No Long Claws: An Analog of the Gy\'{a}rf\'{a}s' Path Argument}},
booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
pages = {93:1--93:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-235-8},
ISSN = {1868-8969},
year = {2022},
volume = {229},
editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16434},
URN = {urn:nbn:de:0030-drops-164343},
doi = {10.4230/LIPIcs.ICALP.2022.93},
annote = {Keywords: Max Independent Set, subdivided claw, QPTAS, subexponential-time algorithm}
}
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Keywords: |
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Max Independent Set, subdivided claw, QPTAS, subexponential-time algorithm |
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Collection: |
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49th International Colloquium on Automata, Languages, and Programming (ICALP 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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28.06.2022 |
