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arXiv · 1303.1872

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

Lei Wang·Xiaodong Wang·Yingjie Wu·Daxin Zhu
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Abstract

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-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 $O(nmr)$.

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Lei Wang, Xiaodong Wang, Yingjie Wu, Daxin Zhu. 2013-03-08. An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains. https://arxiv.org/abs/1303.1872

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