An ETH-tight Exact Algorithm for Euclidean TSP

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

Research output: Contribution to journalArticleAcademicpeer-review

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 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 languageEnglish
Pages (from-to)740-760
Number of pages21
JournalSIAM Journal on Computing
Volume52
Issue number3
DOIs
Publication statusPublished - 30 Jun 2023

Keywords

  • Euclidean traveling salesman
  • separator theroem
  • subexponential algorithm

Fingerprint

Dive into the research topics of 'An ETH-tight Exact Algorithm for Euclidean TSP'. Together they form a unique fingerprint.

Cite this