A Marriage Theorem Based-Algorithm for Solving Sudoku

Abstract

Millions of people around the world are solving a complex constraint satisfaction problem although they do not know. This problem is a famous game known as Sudoku puzzle and it consists in filling a n2 × n2 grid, composed by n columns, n rows and n sub-grids, each one containing different digits from 1 to n2. In this paper, we propose an exact algorithm based on Hall's marriage theorem in order to solve it. After applied our proposed method, we have noticed that some instances with particular features are possible to solve. The algorithm is quite simple to code it and good results are reached solving some instances. The unresolved ones as result of the application of the algorithm is generated an equivalent problem to the original one, but more easiest to solve. We illustrate the experimental evaluation comparing with another complete methods.