# A Gap-ETH-Tight Approximation Scheme for Euclidean TSP

@article{KisfaludiBak2022AGA,
title={A Gap-ETH-Tight Approximation Scheme for Euclidean TSP},
author={S{\'a}ndor Kisfaludi-Bak and Jesper Nederlof and Karol Wegrzycki},
journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)},
year={2022},
pages={351-362}
}
• Published 7 November 2020
• Computer Science
• 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
We revisit the classic task of finding the shortest tour of $n$, points in d-dimensional Euclidean space, for any fixed constant $d\geqslant 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that computes a $(1+\varepsilon){-}$ approximate tour, under a plausible assumption, Specifically, we give an algorithm that runs in $2^{\mathcal{O}(1/\varepsilon^{d-1})}n\log n$ time. This improves the previously smallest dependence on $\varepsilon$ in the running…
1 Citations

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