The first part of the present paper is preliminaries . at the second part we show a lemma as follows : supposing s1 , s2 , . . . are strictly increasing sequences , then there exists a strictly increasing sequence t such that for any i , si and t contain a common subsequence having upper density 1 in t . using the lemma we give a chaotic form more rigorous than distribution chaos in a sequence 本文第一部分介绍有关的预备知识;第二部分首先证明了一个关键性引理:对于给定的可数(包括有限)个严格递增的正整数序列s _ 1 , s _ 2 , … ,可以找到某一个严格递增的正整数序列t ,使得对于每一个i = 1 , 2 , … ,序列s _ i与序列t有一个共同的子序列,它在序列t中的上密度为1 。
Finally , the ability of applying the approved aco algorithm to msa is studied . the idea of divide - and - conquer is adopted to improving the progressive algorithm and the longest common subsequence of multiple sequences is proposed as the partition points of multiple sequences . also , the paper presents how to solve the longest common subsequence of multiple sequences by the approved aco algorithm for mcp 最后,本文对改进的蚁群优化算法在多序列比对问题上的应用进行了研究,采取分治思想改进现有的progressive算法,提出利用最长公共子序列进行多序列分割的策略,并给出怎样利用解决最大团问题的蚁群优化算法求解多序列的最长公共子序列的方法。