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The Problem of Finding Several Given Diameter Spanning Trees of Maximum Total Weight in a Complete Graph

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Analysis of Images, Social Networks and Texts (AIST 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14486))

Abstract

We consider the following NP-hard problem. Given an undirected complete edge-weighted graph and positive integers m, D, the goal is to find m edge-disjoint spanning trees with diameter D of maximum total weight in complete undirected graph. We propose an \(\mathcal O(n^2)\)-time approximation algorithm for the problem, where n is the number of vertices in the input graph. For the case when edge weights are randomly uniformly chosen from the interval (0; 1), we prove sufficient conditions under which the proposed algorithm gives asymptotically optimal solutions.

The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project FWNF-2022-0019).

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, prosp. Akad. Koptyuga, 4, 630090, Novosibirsk, Russia

    E. Kh. Gimadi

  2. Novosibirsk State University, Pirogova, 2, 630090, Novosibirsk, Russia

    E. Kh. Gimadi & A. A. Shtepa

Authors
  1. E. Kh. Gimadi
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  2. A. A. Shtepa
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Corresponding author

Correspondence to E. Kh. Gimadi .

Editor information

Editors and Affiliations

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

    Dmitry I. Ignatov

  2. Krasovskii Institute of Mathematics and Mechanics of Russian Academy of Sciences, Yekaterinburg, Russia

    Michael Khachay

  3. University of Oslo, Oslo, Norway

    Andrey Kutuzov

  4. American University of Armenia, Yerevan, Armenia

    Habet Madoyan

  5. Artificial Intelligence Research Institute, Moscow, Russia

    Ilya Makarov

  6. University of Hamburg, Hamburg, Germany

    Irina Nikishina

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

    Alexander Panchenko

  8. Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates

    Maxim Panov

  9. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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

    Andrey V. Savchenko

  11. Apptek, Aachen, Germany

    Evgenii Tsymbalov

  12. Kazan Federal University, Kazan, Russia

    Elena Tutubalina

  13. MTS AI, Moscow, Russia

    Sergey Zagoruyko

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Gimadi, E.K., Shtepa, A.A. (2024). The Problem of Finding Several Given Diameter Spanning Trees of Maximum Total Weight in a Complete Graph. In: Ignatov, D.I., et al. Analysis of Images, Social Networks and Texts. AIST 2023. Lecture Notes in Computer Science, vol 14486. Springer, Cham. https://doi.org/10.1007/978-3-031-54534-4_24

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  • DOI: https://doi.org/10.1007/978-3-031-54534-4_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-54533-7

  • Online ISBN: 978-3-031-54534-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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