A dynamic programming solution to a generalized LCS problem

Authors:
Lei Wang;Xiaodong Wang;Yingjie Wu;Daxin Zhu
Affiliations:
Microsoft AdCenter, Bellevue, WA 98004, USA;Faculty of Mathematics & Computer Science, Quanzhou Normal University, China and College of Mathematics & Computer Science, Fuzhou University, Fuzhou, China;College of Mathematics & Computer Science, Fuzhou University, Fuzhou, China;Faculty of Mathematics & Computer Science, Quanzhou Normal University, China
Venue:
Information Processing Letters
Year:
2013

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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 (2011) [1], but we found that their algorithm cannot 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).