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- W4289752195 abstract "We study exact algorithms for Euclidean TSP in $mathbb{R}^d$. In the early 1990s algorithms with $n^{O(sqrt{n})}$ running time were presented for the planar case, and some years later an algorithm with $n^{O(n^{1-1/d})}$ running time was presented for any $dgeq 2$. Despite significant interest in subexponential exact algorithms over the past decade, there has been no progress on Euclidean TSP, except for a lower bound stating that the problem admits no $2^{O(n^{1-1/d-epsilon})}$ algorithm unless ETH fails. Up to constant factors in the exponent, we settle the complexity of Euclidean TSP by giving a $2^{O(n^{1-1/d})}$ algorithm and by showing that a $2^{o(n^{1-1/d})}$ algorithm does not exist unless ETH fails." @default.
- W4289752195 created "2022-08-04" @default.
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- W4289752195 date "2018-07-18" @default.
- W4289752195 modified "2023-09-23" @default.
- W4289752195 title "An ETH-Tight Exact Algorithm for Euclidean TSP" @default.
- W4289752195 doi "https://doi.org/10.48550/arxiv.1807.06933" @default.
- W4289752195 hasPublicationYear "2018" @default.
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