Finding knight´s tours on an M×N chessboard with O(MN) hysteresis McCulloch-Pitts neurons

How can a knight be moved on a chessboard so that the knight visits each square once and only once and goes back to the starting square? The earliest serious attempt to find a knight´s tour on the chessboard was made by L. Euler in 1759 [1]. In this correspondence, a parallel algorithm based on the hysteresis McCulloch-Pitts neurons is proposed to solve the knight´s tour problem. The relation between the traveling salesman problem and the knight´s tour problem is also discussed. A large number of simulation runs were performed to investigate the behavior of the hysteresis McCulloch-Pitts neural model. The purpose of this correspondence is to present a case study-how to successfully represent the combinatorial optimization problems by means of neural network