对最大团问题的HEWN算法分析

The Time Complexity of the HEWN Algorithm for the Maximum Clique Problem is Analyzed

对最大团问题的HEWN(hierarchicaledge-weightnetwork)算法进行了复杂性分析.首先通过分析HEWN的结构特点和所需进行的操作,设计了一种实现HEWN算法的数据结构,指出了在HEWN算法中HEWN的存储宜采用邻接多重表和二叉链表相结合的链表表示法,然后从HEWN的存储结构入手,剖析了HEWN的构造过程,在剖析过程中,通过与MCST(maximumcompletesub-graphtree)比较,指出了当2j>n时潜在的、指数的生成和修改GM的次数存在于HEWN算法中.因而,HEWN算法的时间复杂度是指数的,而不是O(n8.5).

In this paper, the time complexity of the HEWN algorithm for the maximum clique problem is analyzed. Firstly, a sort of data structure to implement the HEWN algorithm is designed by analyzing the structural characters of HEWN and the needed operations. It is pointed out that the storage structure of HEWN should use the linked list which combine adjacency multi-list with binary linked list. And then, the building procedure of HEWN is anatomized by starting with the storage structure of HEWN. In the anatomizing procedure, by comparing with the MCST, it is pointed out that underlying exponential times of creating and modifying GM exists in the HEWN algorithm when 2j〉n. Therefore, the time complexity of the HEWN algorithm is exponential instead of O （n^85）.