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A Criterion of Optimality of Some Parallelization Scheme for Backtrack Search Problem in Binary Trees

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Optimization and Applications (OPTIMA 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1145))

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Abstract

The backtracking is a basic combinatorial search algorithm. As many other deterministic methods it suffers from the high complexity. Fortunately the high performance computing can efficiently cope with this issue. It was observed that the structure of the search tree can dramatically affect the efficiency of a parallel search. We study the complexity of a frontal autonomous scheme for the backtrack search parallelization. In this approach several independent cores perform a number of first steps of the backtrack search. After that each core takes one sub-problem and solves it completely. Then the results are merged to select the best solution. To study the impact of the tree structure on the performance of the frontal autonomous scheme we formalize the notion of a perfectly scalable problem and prove a criterion for a search tree to fit to this class.

Partially supported by Russian fund for basic research, project 18-07-00566, and by Program 2 of Presidium of RAS “Mechanisms for ensuring fault tolerance in modern high-performance and highly reliable computing”.

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Notes

  1. 1.

    By the length of a path we mean the number of edges contained in the path.

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Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Roman Kolpakov

  2. Dorodnicyn Computing Centre of Federal Research Center “Computer Science and Control”, Moscow, Russia

    Roman Kolpakov & Mikhail Posypkin

  3. Moscow Institute of Physics and Technology, Moscow, Russia

    Mikhail Posypkin

  4. Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia

    Mikhail Posypkin

Authors
  1. Roman Kolpakov
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  2. Mikhail Posypkin
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Corresponding author

Correspondence to Roman Kolpakov .

Editor information

Editors and Affiliations

  1. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  2. Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  3. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

  4. FRC CSC RAS, Moscow, Russia

    Mikhail Posypkin

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Kolpakov, R., Posypkin, M. (2020). A Criterion of Optimality of Some Parallelization Scheme for Backtrack Search Problem in Binary Trees. In: Jaćimović, M., Khachay, M., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2019. Communications in Computer and Information Science, vol 1145. Springer, Cham. https://doi.org/10.1007/978-3-030-38603-0_33

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  • DOI: https://doi.org/10.1007/978-3-030-38603-0_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38602-3

  • Online ISBN: 978-3-030-38603-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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