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Random Permutations, Random Sudoku Matrices and Randomized Algorithms (1312.0192v1)

Published 1 Dec 2013 in math.CO, cs.DS, and math.PR

Abstract: Some randomized algorithms, used to obtain a random $n2 \times n2$ Sudoku matrix, where $n$ is a natural number, is reviewed in this study. Below is described the set $\Pi_n$ of all $(2n) \times n$ matrices, consisting of elements of the set $\mathbb{Z}_n ={ 1,2,\ldots ,n}$, such that every row is a permutation. It is proved that such matrices would be particularly useful in developing efficient algorithms in generating Sudoku matrices. An algorithm to obtain random $\Pi_n$ matrices is presented in this paper. The algorithms are evaluated according to two criteria - probability evaluation, and time evaluation. This type of criteria is interesting from both theoretical and practical point of view because they are particularly useful in the analysis of computer programs.

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