A New Algorithm for Maximal Compatible Classes Based on Matrix

It is important to search the maximal compatible classes of compatible relation and the maximum complete-subgraphs of simple graph,which can be used in data mining,management decision-making and some specific relations.This paper first analyzes the paths length of maximum complete-subgraph,and then presents a theorem of the paths length of maximum about the complete-subgraph and its path length.Furthermore,the paper gives an algorithm for searching maximum complete-subgraph by the theorem and matrix of the path length.According to the correspondence between the maximal compatible classes of compatible relation and the maximum complete-subgraphs of simple graph,the algorithm can be applied to find maximal compatible classes of compatible relations as well.