Efficient Algorithms for the Flexible Longest Common Subsequence Problem

Given two sequences, the traditional longest common subsequence (LCS) problem is to obtain the common subsequence with the maximum number of matches, without considering the continuity of the matched characters. However, in many applications, the matching results with higher continuity are more meaningful than the sparse ones, even if the number of matched characters is a little lower. Accordingly, we define a new variant of the LCS problem, called the flexible longest common subsequence (FLCS) problem. In this paper, we design a scoring function to estimate the continuity of a matching result between two strings. We show that the optimal solution of FLCS can be determined in O(n) time, where n denotes the longer length of the two input sequences. Therefore, the results in this paper offer a new efficient tool for sequence analysis.