Fully incremental LCS computation

Authors:
Yusuke Ishida;Shunsuke Inenaga;Ayumi Shinohara;Masayuki Takeda
Affiliations:
Department of Informatics, Kyushu University 33, Fukuoka, Japan;Department of Informatics, Kyushu University 33, Fukuoka, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Department of Informatics, Kyushu University 33, Fukuoka, Japan
Venue:
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Year:
2005

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Abstract

Sequence comparison is a fundamental task in pattern matching. Its applications include file comparison, spelling correction, information retrieval, and computing (dis)similarities between biological sequences. A common scheme for sequence comparison is the longest common subsequence (LCS) metric. This paper considers the fully incremental LCS computation problem as follows: For any strings A,B and characters a,b, compute LCS(aA, B), LCS(A, bB), LCS(Aa, B), and LCS(A, Bb), provided that L=LCS(A, B) is already computed. We present an efficient algorithm that computes the four LCS values above, in O(L) or O(n) time depending on where a new character is added, where n is the length of A. Our algorithm is superior in both time and space complexities to the previous known methods.