基于CHNN的地图四着色算法

Map Four-coloring Algorithm Based on CHNN

在地图四着色理论的基础上,使用霍普菲尔德神经网络方法设计了一个能够进行四着色的实用算法,可以对多达100个区域的地图进行四着色。可以将区域地图转化为最大可平面图,并根据顶点集进行霍普菲尔德网络设计。经过仿真实验,总结出了不同的顶点数所使用的不同参数,解决了非确定性的霍普菲尔德神经网络方法的成功率问题。实验结果揭示出霍普菲尔德神经网络在图论研究中的可行的计算方法和良好效果。

Based on the map four coloring theory with the help of continuous Hopfield neural net-work （CHNN）method,we designed a practical algorithm which could realize four coloring in one hundred areas of a map.By this algorithm,a regional map could be transformed into a maximal planar graph where the network of Hopfield could be designed according to the vertex set. Through simulation experiment,different parameters of different vertex numbers were summa-rized,and the problem of successful rate by the non-deterministic Hopfield Neural Network method was solved.Our experiments revealed the feasible calculating method and good results of CHNN in the study of graph theory.