An ETH-Tight Exact Algorithm for Euclidean TSP

We study exact algorithms for Euclidean TSP in R
^d
. In the early 1990s algorithms with n
^O(√n)
running time were presented for the planar case, and some years later an algorithm with n
^O(n1-1/d)
running time was presented for any d ≥ 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-ε
) algorithm unless ETH fails. Up to constant factors in the exponent, we settle the complexity of Euclidean TSP by giving a 2
^O(n1-1/d)
algorithm and by showing that a 2
^o(n1-1/d)
algorithm does not exist unless ETH fails.