LIPIcs.ESA.2023.33.pdf
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Polynomial-Time Approximation of Independent Set Parameterized by Treewidth
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31st Annual European Symposium on Algorithms (ESA 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-08-30
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Acknowledgements
The research presented in this paper was initiated partially during the trimester on Discrete Optimization at Hausdorff Research Institute for Mathematics (HIM) in Bonn, Germany.
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Parinya Chalermsook, Fedor Fomin, Thekla Hamm, Tuukka Korhonen, Jesper Nederlof, and Ly Orgo. Polynomial-Time Approximation of Independent Set Parameterized by Treewidth. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 33:1-33:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ESA.2023.33
https://doi.org/10.4230/LIPIcs.ESA.2023.33
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Approximation algorithms analysis
- Theory of computation → Graph algorithms analysis
Keywords
- Maximum Independent Set
- Treewidth
- Approximation Algorithms
- Parameterized Approximation
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References
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