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A Given Diameter MST on a Random Graph

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

We give a new approximation polynomial time algorithm for one of the intractable problem of finding given-diameter Minimum Spanning Tree (MST) on n-vertex complete graph with randomly weighted edges. A significant advantage of this algorithm is that it turned out to be well suited for finding several edge-disjoint MST of a given diameter. A probabilistic analysis was performed under conditions that edge weights of given graph are identically independent uniformly distributed random variables on an segment \([a_n; b_n]\), \(a_n>0\). Sufficient conditions of asymptotic optimality are presented. It is also noteworthy that the new algorithmic approach to solve the problem of finding a given-diameter MST both on directed and undirected graphs.

Supported by the program of fundamental scientific researches of the SB RAS No. I.5.1., project No. 0314-2019-0014, and by the Russian Foundation for Basic Research, project No. 20-31-90091.

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Author information

Authors and Affiliations

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

    Edward K. Gimadi

  2. Novosibirsk State University, Pirogova, 1, Novosibirsk, Russia

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

Authors
  1. Edward K. Gimadi
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  2. Aleksandr S. Shevyakov
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  3. Alexandr A. Shtepa
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Corresponding author

Correspondence to Alexandr A. Shtepa .

Editor information

Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

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

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Gimadi, E.K., Shevyakov, A.S., Shtepa, A.A. (2020). A Given Diameter MST on a Random Graph. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_9

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