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- W2080249901 abstract "We apply Monte Carlo simulations to count the numbers of solutions of two well-known combinatorial problems: the $N$-queens problem and Latin-square problem. The original system is first converted to a general thermodynamic system, from which the number of solutions of the original system is obtained by using the method of computing the partition function. Collective moves are used to further accelerate sampling: swap moves are used in the $N$-queens problem and a cluster algorithm is developed for the Latin squares. The method can handle systems of ${10}^{4}phantom{rule{0.3em}{0ex}}text{degrees}$ of freedom with more than ${10}^{10phantom{rule{0.2em}{0ex}}000}$ solutions." @default.
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- W2080249901 date "2009-01-08" @default.
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- W2080249901 title "Counting solutions for the<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math>-queens and Latin-square problems by Monte Carlo simulations" @default.
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- W2080249901 doi "https://doi.org/10.1103/physreve.79.016703" @default.
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