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On Given Diameter MST Problem on Random Input Data

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

We give an approximation deterministic algorithm for solving the Random MST with given diameter of directed graph. The problem is NP-hard. Algorithm has a quadratic time complexity. A probabilistic analysis was performed under conditions that edge weights of given graph are identically independent uniformly distributed random variables on an interval with positive ends. Sufficient conditions of asymptotic optimality are presented.

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Acknowledgments

The authors are 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 of the Russian Federation under the 5–100 Excellence Programme.

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Authors and Affiliations

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

    Edward Kh. Gimadi

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

    Edward Kh. Gimadi & Ekaterina Yu. Shin

Authors
  1. Edward Kh. Gimadi
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  2. Ekaterina Yu. Shin
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Corresponding author

Correspondence to Edward Kh. Gimadi .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Gimadi, E.K., Shin, E.Y. (2019). On Given Diameter MST Problem on Random Input Data. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_3

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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