Longest common subsequence in at least k length order-isomorphic substrings

Abstract

We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least k length substrings. First, we show an O(mn) time algorithm for the problem which gives a better worst-case running time than existing algorithms, where m and n are lengths of the input strings. Furthermore, we mainly consider the LCS in at least k length order-isomorphic substrings problem. We show that the problem can also be solved in O(mn) worst-case time by an easy-to-implement algorithm.