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

Sen Bai, Guibin Zhu, Jian Huang
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引用次数: 6

Abstract

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.
(1,2,2)-广义Knight漫游问题的一种智能算法
在[离散应用数学158(2010)1727-1731]中,我们证明了3×4q×4p(其中q≥2和p≥2为整数)棋盘允许一个封闭(1,2,2)-广义骑士游(GKT)。本文证明了一个大小为L×4q×4p且L≥3且L≠4,q≥2,p≥2的棋盘必须包含一个闭的(1,2,2)-GKT。然后,基于已证明的引理和定理,提出了在L×4q×4p棋盘上寻找闭(1,2,2)-GKT的智能算法。提出的在L×4q×4p棋盘上构造结构化(1,2,2)-GKT哈密顿循环的算法可以很容易地在智能中实现。最后,将GKT哈密顿循环应用于视频加密,仿真实验结果表明GKT置乱适合于感知视频加密。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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