A Diagonal-Based Algorithm for the Constrained Longest Common Subsequence Problem

Abstract

Given two sequences A and B of lengths m and n, respectively, and another constrained sequence C with length r, the constrained longest common subsequence (CLCS) problem is to find the longest common subsequence (LCS) of A and B with the constraint that C is contained as a subsequence in the answer. Based on the diagonal concept for finding the LCS length, proposed by Nakatsu et al., this paper proposes an algorithm for obtaining the CLCS length efficiently in O\((rL(m-L))\) time and O(mr) space, where L denotes the CLCS length. According to the experimental result, the proposed algorithm outperforms the previously CLCS algorithms.