An ETH-Tight Exact Algorithm for Euclidean TSP
Mark de Berg, Hans L. Bodlaender, S\'andor Kisfaludi-Bak, Sudeshna, Kolay

TL;DR
This paper presents a new exact algorithm for Euclidean TSP that is optimal up to constants, matching the known lower bounds and settling the problem's complexity status.
Contribution
The authors introduce an ETH-tight exact algorithm for Euclidean TSP in any dimension, establishing both upper and lower bounds.
Findings
Algorithm runs in $2^{O(n^{1-1/d})}$ time.
No faster algorithm exists unless ETH fails.
Settles the complexity of Euclidean TSP up to constants.
Abstract
We study exact algorithms for Euclidean TSP in . In the early 1990s algorithms with running time were presented for the planar case, and some years later an algorithm with running time was presented for any . 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 algorithm unless ETH fails. Up to constant factors in the exponent, we settle the complexity of Euclidean TSP by giving a algorithm and by showing that a algorithm does not exist unless ETH fails.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Vehicle Routing Optimization Methods
