Efficient merged longest common subsequence algorithms for similar sequences

Given a pair of merging sequences A and B, and a target sequence T , the merged longest common subsequence (MLCS) problem is to find out a longest common subsequence (LCS) between sequences E(A,B) and T , where E(A,B) is obtained from merging two subsequences of A and B. In this paper, we propose an algorithm for solving the MLCS problem in O(L(r − L + 1)m) time, where r and L denote the lengths of T and MLCS, respectively, and m denotes the minimum length of A and B. From the time complexity, it is clear that our algorithm is extremely efficient when T and E(A,B) are very similar. Experimental results show that our algorithm is faster than other previously published MLCS algorithms for sequences with high similarity.