License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ESA.2020.66
URN: urn:nbn:de:0030-drops-129329
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Kowalik, Łukasz ; Li, Shaohua ; Nadara, Wojciech ; Smulewicz, Marcin ; Wahlström, Magnus

Many Visits TSP Revisited

LIPIcs-ESA-2020-66.pdf (1.0 MB)


We study the Many Visits TSP problem, where given a number k(v) for each of n cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits each city v exactly k(v) times. The currently fastest algorithm is due to Berger, Kozma, Mnich and Vincze [SODA 2019, TALG 2020] and runs in time and space O*(5ⁿ). They also show a polynomial space algorithm running in time O(16^{n+o(n)}). In this work, we show three main results:
- A randomized polynomial space algorithm in time O*(2^n D), where D is the maximum distance between two cities. By using standard methods, this results in a (1+ε)-approximation in time O*(2ⁿε^{-1}). Improving the constant 2 in these results would be a major breakthrough, as it would result in improving the O*(2ⁿ)-time algorithm for Directed Hamiltonian Cycle, which is a 50 years old open problem.
- A tight analysis of Berger et al.’s exponential space algorithm, resulting in an O*(4ⁿ) running time bound.
- A new polynomial space algorithm, running in time O(7.88ⁿ).

BibTeX - Entry

  author =	{Łukasz Kowalik and Shaohua Li and Wojciech Nadara and Marcin Smulewicz and Magnus Wahlstr{\"o}m},
  title =	{{Many Visits TSP Revisited}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{66:1--66:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-129329},
  doi =		{10.4230/LIPIcs.ESA.2020.66},
  annote =	{Keywords: many visits traveling salesman problem, exponential algorithm}

Keywords: many visits traveling salesman problem, exponential algorithm
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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