A Fast On-Line Algorithm for the Longest Common Subsequence Problem with Constant Alphabet

Yoshifumi SAKAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.1   pp.354-361
Publication Date: 2012/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.354
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Algorithms and Data Structures
algorithm,  string comparison,  longest common subsequence,  on-line algorithm,  

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This article presents an algorithm that solves an on-line version of the longest common subsequence (LCS) problem for two strings over a constant alphabet in O(d+n) time and O(m+d) space, where m is the length of the shorter string, the whole of which is given to the algorithm in advance, n is the length of the longer string, which is given as a data stream, and d is the number of dominant matches between the two strings. A new upper bound, O(p(m-q)), of d is also presented, where p is the length of the LCS of the two strings, and q is the length of the LCS of the shorter string and the m-length prefix of the longer string.