Abstract
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. A simple 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 O(nmdt), where \(t=\prod \limits _{1\le i\le d}l_i\).
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Acknowledgments
This work was supported by the Science and Technology Foundation of Quanzhou under Grant No. 2013Z38, Fujian Provincial Key Laboratory of Data-Intensive Computing and Fujian University Laboratory of Intelligent Computing and Information Processing.
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Zhu, D., Wu, Y., Wang, X. (2015). A Dynamic Programming Algorithm for a Generalized LCS Problem with Multiple Subsequence Inclusion Constraints. In: Hsu, CH., Xia, F., Liu, X., Wang, S. (eds) Internet of Vehicles - Safe and Intelligent Mobility. IOV 2015. Lecture Notes in Computer Science(), vol 9502. Springer, Cham. https://doi.org/10.1007/978-3-319-27293-1_38
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