A Polynomial Time Algorithm for a Generalized Longest Common Subsequence Problem

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusive constraints. For the two input sequences X and Y of lengths n and m, and a set of d constraints P = {P1, · · · , Pd} of total length r, the problem is to find a common subsequence Z of X and Y excluding each of constraint string in P as a substring and the length of Z is maximized. A very simple dynamic programming algorithm to this problem is presented in this paper. The correctness of the new algorithm is demonstrated. The time and space complexities of the new algorithm are both O(nmr).