Efficient Sparse Dynamic Programming for the Merged LCS Problem

Detecting the interleaving relationship between sequences is a new research topic which begins to draw much attention. Recently, Huang et al. proposed the merged LCS model, which can be realized as finding the longest common subsequence between a target sequence and two merging sequences. Given the targe sequence T and two merging sequences A and B, Huang et al. gave an O(nmr)-time and O(mr)-space algorithm for solving this problem, where n, m and r denote the length of T , the longer and shorter length of A and B, respectively. In this paper, we propose an improved O(Lnr)-time and O(m + Lr)-space algorithm for solving the merged LCS problem, where L denotes the length of the optimal solution. Compared with Huang’s results, our algorithms are more efficient for applications where L could be relatively small.