An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains [article]

Lei Wang, Xiaodong Wang, Yingjie Wu, Daxin Zhu
2013 arXiv   pre-print
In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences X and Y of lengths n and m, and a set of d constrains P={P_1,...,P_d} of total length r, the problem is to find a common subsequence Z of X and Y excluding each of constrain string in P as a substring and the length of Z is maximized. The problem was declared to be NP-hard1, but we finally found that this is not true. A new dynamic programming
more » ... tion for this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is O(nmr).
arXiv:1303.1872v1 fatcat:uv2t66kfajcfzjovi5iibihqni