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arXiv · 1506.00063

An Efficient Dynamic Programming Algorithm for STR-IC-SEQ-EC-LCS Problem

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

In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length $s$ must be included as a substring and the other constraining sequence of length $t$ must be excluded as a subsequence of two main sequences and the length of the result must be maximal. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and the given two constraining sequences of length $s$ and $t$, we present an $O(nmst)$ time dynamic programming algorithm for solving the new generalized longest common subsequence problem. The time complexity can be reduced further to cubic time in a more detailed analysis. The correctness of the new algorithm is proved.

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Daxin Zhu, Lei Wang, Yingjie Wu, Xiaodong Wang. 2015-05-30. An Efficient Dynamic Programming Algorithm for STR-IC-SEQ-EC-LCS Problem. https://arxiv.org/abs/1506.00063

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