Solving Sudoku Using Combined Message Passing Algorithms

In this paper we apply message-passing algorithms to solve Sudoku puzzles. We provide explicit expression for the sum-product algorithm and the max-product algorithm and analyze the difference between the algorithms in terms of performance and efficiency. The failure of the max-product algorithm when been applied to Sudoku problem is due to the existence of stopping-sets. We show empirically that the performance of the max-product algorithm in the case of Sudoku can be improved by adding redundant constraints. We show that applying the sum-product to the stopping-set obtained by the max-product, can lead to effective and efficient puzzle-solving method.