A Fast On-Line Algorithm for the Longest Common Subsequence Problem with Constant Alphabet
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 in 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 in-length prefix of the longer string.
on-line algorithm algorithm longest common subsequence string comparison