4 research outputs found

    An ETH-Tight Exact Algorithm for Euclidean TSP

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    We study exact algorithms for {\sc Euclidean TSP} in Rd\mathbb{R}^d. In the early 1990s algorithms with nO(n)n^{O(\sqrt{n})} running time were presented for the planar case, and some years later an algorithm with nO(n1−1/d)n^{O(n^{1-1/d})} running time was presented for any d≥2d\geq 2. Despite significant interest in subexponential exact algorithms over the past decade, there has been no progress on {\sc Euclidean TSP}, except for a lower bound stating that the problem admits no 2O(n1−1/d−ϵ)2^{O(n^{1-1/d-\epsilon})} algorithm unless ETH fails. Up to constant factors in the exponent, we settle the complexity of {\sc Euclidean TSP} by giving a 2O(n1−1/d)2^{O(n^{1-1/d})} algorithm and by showing that a 2o(n1−1/d)2^{o(n^{1-1/d})} algorithm does not exist unless ETH fails.Comment: To appear in FOCS 201
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