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={P1​,...,Pd​}
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-hard\cite{1}, but we
finally found that this is not true. A new dynamic programming solution 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).Comment: arXiv admin note: substantial text overlap with arXiv:1301.718