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arXiv · 1301.7183

A Dynamic Programming Solution to a Generalized LCS Problem

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

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 $O(nmr)$.

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Lei Wang, Xiaodong Wang, Yingjie Wu, Daxin Zhu. 2013-01-30. A Dynamic Programming Solution to a Generalized LCS Problem. https://arxiv.org/abs/1301.7183

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