An ETH-tight Exact Algorithm for Euclidean TSP
de Berg, Mark; Bodlaender, Hans L.; Kisfaludi-Bak, Sándor; Kolay, Sudeshna
(2023) SIAM Journal on Computing, volume 52, issue 3, pp. 740 - 760
(Article)
Abstract
We study exact algorithms for Metric TSP in ℝd. 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
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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).
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Keywords: Euclidean traveling salesman, separator theroem, subexponential algorithm, Taverne, General Computer Science, General Mathematics
ISSN: 0097-5397
Publisher: Society for Industrial and Applied Mathematics Publications
Note: Funding Information: *Received by the editors January 4, 2022; accepted for publication (in revised form) February 6, 2023; published electronically June 5, 2023. An earlier version of this article appeared in the Proceedings of the 59th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2018, IEEE Computer Society, 2018, pp. 450--461, and the article shares content with the third author's thesis prepared at Technische Universiteit Eindhoven, Department of Mathematics and Computer Science, 2019. https://doi.org/10.1137/22M1469122 Funding: This work was supported by the NETWORKS project funded by the Netherlands Organization for Scientific Research under grant 024.002.003. \dagger Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlands (m.t.d.berg@tue.nl). \ddagger Department of Computer Science, Utrecht University, Utrecht 3508 TB, The Netherlands (h.l.bodlaender@uu.nl). \S Department of Computer Science, Aalto University, Espoo FI-00076, Finland (sandor.kisfaludi-bak@aalto.fi). \P Indian Institute of Technology Kharagpur, Kharagpur, India (skolay@cse.iitkgp.ac.in). Publisher Copyright: Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
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