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 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.