In this paper, we revisit a recent variant of the longest common subsequence (LCS) problem, the string-excluding constrained LCS (STR-EC-LCS) problem, which was first addressed by Chen and Chao (J Comb Optim 21(3):383–392, 2011). Given two sequences \documentclass[12pt]{minimal}
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\begin{document}$$X$$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$$Y$$\end{document} of lengths \documentclass[12pt]{minimal}
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\begin{document}$$m$$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$$n,$$\end{document} respectively, and a constraint string \documentclass[12pt]{minimal}
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\begin{document}$$P$$\end{document} of length \documentclass[12pt]{minimal}
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\begin{document}$$r,$$\end{document} we are to find a common subsequence \documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} of \documentclass[12pt]{minimal}
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\begin{document}$$X$$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$$Y$$\end{document} which excludes \documentclass[12pt]{minimal}
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\begin{document}$$P$$\end{document} as a substring and the length of \documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} is maximized. In fact, this problem cannot be correctly solved by the previously proposed algorithm. Thus, we give a correct algorithm with \documentclass[12pt]{minimal}
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\begin{document}$$O(mnr)$$\end{document} time to solve it. Then, we revisit the STR-EC-LCS problem with multiple constraints \documentclass[12pt]{minimal}
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\begin{document}$$\{ P_1, P_2, \ldots , P_k \}.$$\end{document} We propose a polynomial-time algorithm which runs in \documentclass[12pt]{minimal}
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\begin{document}$$O(mnR)$$\end{document} time, where \documentclass[12pt]{minimal}
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\begin{document}$$R = \sum _{i=1}^{k} |P_i|,$$\end{document} and thus it overthrows the previous claim of NP-hardness.
