Treewidth Inapproximability and Tight ETH Lower Bound

Édouard Bonnet

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arXiv · 2406.11628

Treewidth Inapproximability and Tight ETH Lower Bound

Édouard Bonnet

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Abstract

We present a simple, self-contained, linear reduction from 3-SAT to Treewidth. Specifically, it shows that 1.00005-approximating Treewidth is NP-hard, and solving Treewidth exactly requires $2^{\Omega(n)}$ time, unless the Exponential-Time Hypothesis fails. We further derive, under the latter assumption, that there are some constants $\delta > 1$ and $c>0$ such that $\delta$-approximating Treewidth requires time $2^{\Omega(n/\log^c n)}$.

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BibTeX RIS

Édouard Bonnet. 2024-06-17. Treewidth Inapproximability and Tight ETH Lower Bound. https://arxiv.org/abs/2406.11628

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