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# Polynomial-Time Approximation of Independent Set Parameterized by Treewidth

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LIPIcs.ESA.2023.33.pdf
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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.

## Cite As

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

## 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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