Treewidth Inapproximability and Tight ETH Lower Bound
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916808006565888 |
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| author | Bonnet, Édouard |
| author_facet | Bonnet, Édouard |
| contents | 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 $2^{Ω(n)}$ time, unless the Exponential-Time Hypothesis fails. We further derive, under the latter assumption, that there are some constants $δ> 1$ and $c>0$ such that $δ$-approximating Treewidth requires time $2^{Ω(n/\log^c n)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Treewidth Inapproximability and Tight ETH Lower Bound Bonnet, Édouard Computational Complexity Discrete Mathematics Data Structures and Algorithms Combinatorics 68Q17 F.2.2 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 $2^{Ω(n)}$ time, unless the Exponential-Time Hypothesis fails. We further derive, under the latter assumption, that there are some constants $δ> 1$ and $c>0$ such that $δ$-approximating Treewidth requires time $2^{Ω(n/\log^c n)}$. |
| title | Treewidth Inapproximability and Tight ETH Lower Bound |
| topic | Computational Complexity Discrete Mathematics Data Structures and Algorithms Combinatorics 68Q17 F.2.2 |
| url | https://arxiv.org/abs/2406.11628 |