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On Modification of an Asymptotically Optimal Algorithm for the Maximum Euclidean Traveling Salesman Problem

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Book cover Analysis of Images, Social Networks and Texts (AIST 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11179))

Abstract

The known asymptotically optimal algorithm for the Euclidean maximum Traveling Salesman Problem by Serdukov builds approximate solution for the problem around the maximum-weight perfect matching. In this paper we are going to discuss an asymptotically optimal algorithm for the Euclidean maximum TSP with running-time \(O(n^3)\), that uses a maximum weight cycle cover of the initial graph as a foundation for constructing the TSP solution. We also prove a number of structural results for the optima of some maximization problems in normed spaces, which follow from the algorithm.

Supported by Russian Science Foundation (project 16-11-10041).

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References

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Edward Kh. Gimadi & Oxana Yu. Tsidulko

  2. Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia

    Edward Kh. Gimadi & Oxana Yu. Tsidulko

Authors
  1. Edward Kh. Gimadi
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  2. Oxana Yu. Tsidulko
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Corresponding author

Correspondence to Oxana Yu. Tsidulko .

Editor information

Editors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Wil M. P. van der Aalst

  2. University of Ljubljana, Ljubljana, Slovenia

    Vladimir Batagelj

  3. University of Mannheim, Mannheim, Germany

    Goran Glavaš

  4. National Research University Higher School of Economics, Moscow, Russia

    Dmitry I. Ignatov

  5. Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  6. National Research University Higher School of Economics, Moscow, Russia

    Sergei O. Kuznetsov

  7. National Research University Higher School of Economics , Saint Petersburg, Russia

    Olessia Koltsova

  8. National Research University Higher School of Economics, Moscow, Russia

    Irina A. Lomazova

  9. Moscow State University, Moscow, Russia

    Natalia Loukachevitch

  10. Loria, Vandoeuvre lès Nancy, France

    Amedeo Napoli

  11. University of Hamburg, Hamburg, Germany

    Alexander Panchenko

  12. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  13. Ca Foscari University of Venice, Venice, Italy

    Marcello Pelillo

  14. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Andrey V. Savchenko

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Gimadi, E.K., Tsidulko, O.Y. (2018). On Modification of an Asymptotically Optimal Algorithm for the Maximum Euclidean Traveling Salesman Problem. In: van der Aalst, W., et al. Analysis of Images, Social Networks and Texts. AIST 2018. Lecture Notes in Computer Science(), vol 11179. Springer, Cham. https://doi.org/10.1007/978-3-030-11027-7_27

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  • DOI: https://doi.org/10.1007/978-3-030-11027-7_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11026-0

  • Online ISBN: 978-3-030-11027-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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