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Approximation Algorithms for the Maximum m-Peripatetic Salesman Problem

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Analysis of Images, Social Networks and Texts (AIST 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10716))

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Abstract

We consider the maximum m-Peripatetic Salesman Problem (MAX m-PSP), which is a natural generalization of the classic Traveling Salesman Problem. The problem is strongly NP-hard. In this paper we propose two polynomial approximation algorithms for the MAX m-PSP with different and identical weight functions, correspondingly. We prove that for random inputs uniformly distributed on the interval [a, b] these algorithms are asymptotically optimal for \(m=o(n)\). This means that with high probability their relative errors tend to zero as the number n of the vertices of the graph tends to infinity. The results remain true for the distributions of inputs that minorize the uniform distribution.

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Acknowledgments

The authors are supported by the Russian Foundation for Basic Research grants 16-31-00389 and 15-01-00976, Russian Ministry of Science and Education under 5-100 Excellence Program, and the grant of Presidium of RAS (program 8, project 227).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090, Novosibirsk, Russia

    Edward Kh. Gimadi & Oxana Yu. Tsidulko

  2. Novosibirsk State University, 2 Pirogova Str., 630090, 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. Eindhoven University of Technology, Eindhoven, The Netherlands

    Wil M.P. van der Aalst

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

    Dmitry I. Ignatov

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

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

    Sergei O. Kuznetsov

  5. Skolkovo Institute of Science and Technology, Moscow, Russia

    Victor Lempitsky

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

    Irina A. Lomazova

  7. Moscow State University, Moscow, Russia

    Natalia Loukachevitch

  8. LORIA, Campus Scientifique, Vandœuvre lès Nancy, France

    Amedeo Napoli

  9. University of Hamburg, Hamburg, Germany

    Alexander Panchenko

  10. University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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

    Andrey V. Savchenko

  12. Indiana University, Bloomington, Indiana, USA

    Stanley Wasserman

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Gimadi, E.K., Tsidulko, O.Y. (2018). Approximation Algorithms for the Maximum m-Peripatetic Salesman Problem. In: van der Aalst, W., et al. Analysis of Images, Social Networks and Texts. AIST 2017. Lecture Notes in Computer Science(), vol 10716. Springer, Cham. https://doi.org/10.1007/978-3-319-73013-4_28

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  • DOI: https://doi.org/10.1007/978-3-319-73013-4_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73012-7

  • Online ISBN: 978-3-319-73013-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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