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Linear Systems, Sparse Solutions, and Sudoku
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DOI：10.1109/LSP.2009.2032489.png)
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摘要
En 中文
In this paper, we show that Sudoku puzzles can be formulated and solved as a sparse linear system of equations. We begin by showing that the Sudoku ruleset can be expressed as an underdetermined linear system: Ax = b, where A is of size m x n and n > m. We then prove that the Sudoku solution is the sparsest solution of Ax = b, which can be obtained by norm minimization, i.e. min(x) parallel to x parallel to(0) s.t. Ax = b. Instead of this minimization problem, inspired by the sparse representation literature, we solve the much simpler linear programming problem of minimizing the l(1) norm of, i.e. min(x) parallel to x parallel to(1) s.t. Ax = b, and show numerically that this approach solves representative Sudoku puzzles.
Keyword:
Linear systems
l(0) norm minimization
l(1) norm minimization
sparse representation
Sudoku
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IF:
9.6
论文数:
1.1W
被引数:
1.7W
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