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On Asymptotically Optimal Approach for the Problem of Finding Several Edge-Disjoint Spanning Trees of Given Diameter in an Undirected Graph with Random Edge Weights

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Mathematical Optimization Theory and Operations Research (MOTOR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12755))

Abstract

We consider the intractable problem of finding several edge-disjoint spanning trees of a given diameter in an graph with random edge weights. Earlier, we have implemented an asymptotically optimal approach for this problem in the case of directed graphs. The direct use of this result for the case of undirected graphs turned out to be impossible due to the issues associated with the summation of dependent random variables. In this work we give an \(O(n^2)\)-time algorithm with conditions of asymptotic optimality for the case of undirected graphs.

Supported by the program of fundamental scientific researches of the SB RAS (project 0314-2019-0014), and by the Ministry of Science and Higher Education

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Author information

Authors and Affiliations

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

    Edward Kh. Gimadi

  2. Novosibirsk State University, Novosibirsk, Russia

    Edward Kh. Gimadi, Aleksandr S. Shevyakov & Alexandr A. Shtepa

Authors
  1. Edward Kh. Gimadi
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  2. Aleksandr S. Shevyakov
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  3. Alexandr A. Shtepa
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Editor information

Editors and Affiliations

  1. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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

    Michael Khachay

  3. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, Russia

    Alexander Kazakov

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Gimadi, E.K., Shevyakov, A.S., Shtepa, A.A. (2021). On Asymptotically Optimal Approach for the Problem of Finding Several Edge-Disjoint Spanning Trees of Given Diameter in an Undirected Graph with Random Edge Weights. In: Pardalos, P., Khachay, M., Kazakov, A. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2021. Lecture Notes in Computer Science(), vol 12755. Springer, Cham. https://doi.org/10.1007/978-3-030-77876-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-77876-7_5

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  • Print ISBN: 978-3-030-77875-0

  • Online ISBN: 978-3-030-77876-7

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