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Using the Monte Carlo Method for Fast Simulation of the Number of “Good” Permutations on the SCIT-4 Multiprocessor Computer Complex

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Cybernetics and Systems Analysis Aims and scope

An Erratum to this article was published on 01 March 2016

Abstract

A permutation (s 0 , s 1, ⋯, s N −1) of symbols 0,1, ,⋯ , N − 1 is called “good” if the set (t 0 , t 1,⋯, t N −1) formed by the rule t i= i + s i (mod N),i = 0,1,⋯, N −1, is also a permutation. The author proposes the fast simulation method. Its implementation on the SCIT-4 multiprocessor computer complex makes it possible to evaluate the number of “good” permutations for N ≤ 305 with relative accuracy no greater than 1%. The number of “good” permutations is estimated for N 25, 35, ⋯, 305.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine; Institute of Physics and Technology, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine

    N. Yu. Kuznetsov

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  1. N. Yu. Kuznetsov
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Correspondence to N. Yu. Kuznetsov.

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Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2016, pp. 57–63.

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Kuznetsov, N.Y. Using the Monte Carlo Method for Fast Simulation of the Number of “Good” Permutations on the SCIT-4 Multiprocessor Computer Complex. Cybern Syst Anal 52, 52–57 (2016). https://doi.org/10.1007/s10559-016-9799-0

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