A Dynamic Programming Algorithm for a Generalized LCS Problem with Multiple Subsequence Inclusion Constraints

In this paper, we consider a generalized longest common subsequence problem with multiple subsequence inclusive constraints. For the two input sequences X and Y of lengths n and m, and a set of d constraints $$P=\{P_1,\cdots ,P_d\}$$ of length $$l_i$$ for each $$P_i\in P$$, the problem is to find a common subsequence Z of X and Y including each of constraint string in P as a subsequence and the length of Z is maximized. Ai?źsimple dynamic programming algorithm to this problem is presented in this paper. The correctness of the new algorithm is demonstrated. The time complexities of the new algorithm is Onmdt, where $$t=\prod \limits _{1\le i\le d}l_i$$.

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