An Intelligent Algorithm for the (1,2,2)-Generalized Knight´s Tour Problem

In [Discrete Applied Mathematics 158(2010)1727-1731], we proved that the 3×4q×4p (where q≥2 and p≥2 are integer) chessboard admits a closed (1, 2, 2)-generalized knight´s tour (GKT). In this paper, we prove that a chessboard of size L×4q×4p with L≥3 and L≠4, q≥2 and p≥2 must contain a closed (1, 2, 2)-GKT. Next, an intelligent algorithm based on the proved Lemma and Theorem is proposed to find closed (1, 2, 2)-GKT on L×4q×4p chessboard. The proposed algorithms for constructing structured (1, 2, 2)-GKT Hamiltonian cycle on L×4q×4p chessboard can readily be implemented in intelligence. Finally, the GKT Hamiltonian cycle is applied to video encryption, and simulation experimental results show that the GKT scrambling is suitable for perceptual video encryption.