An ETH-Tight Exact Algorithm for Euclidean TSP

Mark de Berg; Hans L. Bodlaender; Sándor Kisfaludi-Bak; Sudeshna Kolay

doi:10.1137/22M1469122

An ETH-Tight Exact Algorithm for Euclidean TSP

Mark de Berg, Hans L. Bodlaender, Sándor Kisfaludi-Bak, Sudeshna Kolay

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Abstract

We study exact algorithms for Metric TSP in ℝ^d. In the early 1990s, algorithms with (Formula Presented) running time were presented for the planar case, and some years later an algorithm with (Formula Presnted) running time was presented for any d\geqslant 2. Despite significant interest in subexponential exact algorithms over the past decade, there has been no progress on Metric TSP, except for a lower bound stating that the problem admits no (Formula Presented) algorithm unless ETH fails. In this paper we settle the complexity of Metric TSP, up to constant factors in the exponent and under ETH, by giving an algorithm with running time (Formula Presented).

Original language	English
Pages (from-to)	740-760
Number of pages	21
Journal	SIAM JOURNAL ON COMPUTING
Volume	52
Issue number	3
DOIs	https://doi.org/10.1137/22M1469122
Publication status	Published - 2023
MoE publication type	A1 Journal article-refereed

Keywords

Euclidean traveling salesman
separator theroem
subexponential algorithm

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An ETH-Tight Exact Algorithm for Euclidean TSP

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