In this paper, we consider a generalized longest common subsequence problem, the string-excluding constrained LCS problem. For the two input sequences X and Y of lengths n and m, and a constraint string P of length r, the problem is to find a common subsequence Z of X and Y excluding P as a substring and the length of Z is maximized. The problem and its solution were first proposed by Chen and Chao\cite{1}, but we found that their algorithm can not solve the problem correctly. A new dynamic programming solution for the STR-EC-LCS problem is then presented in this paper. The correctness of the new algorithm is proved. The time complexity of the new algorithm is O(nmr).
@article{arxiv.1301.7183,
title = {A Dynamic Programming Solution to a Generalized LCS Problem},
author = {Lei Wang and Xiaodong Wang and Yingjie Wu and Daxin Zhu},
journal= {arXiv preprint arXiv:1301.7183},
year = {2013}
}