Abstract
Locating longest common subsequences is a typical and important problem. The original version of locating longest common subsequences stretches a longer alignment between a query and a database sequence finds all alignments corresponding to the maximal length of common subsequences. However, the original version produces a lot of results, some of which are meaningless in practical applications and rise to a lot of time overhead. In this paper, we firstly define longest common subsequences with limited penalty to compute the longest common subsequences whose penalty values are not larger than a threshold \(\tau \). This helps us to find answers with good locality. We focus on the efficiency of this problem. We propose a basic approach for finding longest common subsequences with limited penalty. We further analyze features of longest common subsequences with limited penalty, and based on it we propose a filter-refine approach to reduce number of candidates. We also adopt suffix array to efficiently generate common substrings, which helps calculating the problem. Experimental results on three real data sets show the effectiveness and efficiency of our algorithms.
This work is partially supported by the NSF of China for Outstanding Young Scholars under grant No. 61322208, the NSF of China under grant Nos. 61272178 and 61572122.
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Notes
- 1.
Notice that, the definition of penalty score of LCS is different from edit distance even when \(\alpha =\beta =1\). The edit distance between two strings represents the minimal number of edit operations transforming from one string to another string, which does not guarantee to find an alignment with longest common subsequences as LCS does.
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Wang, B., Yang, X., Li, J. (2017). Locating Longest Common Subsequences with Limited Penalty. In: Candan, S., Chen, L., Pedersen, T., Chang, L., Hua, W. (eds) Database Systems for Advanced Applications. DASFAA 2017. Lecture Notes in Computer Science(), vol 10178. Springer, Cham. https://doi.org/10.1007/978-3-319-55699-4_12
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