An Efficient Algorithm for LCS Problem between Two Arbitrary Sequences

Abstract

The longest common subsequence (LCS) problem is a classic computer science problem. For the essential problem of computing LCS between two arbitrary sequences s1 and s2, this paper proposes an algorithm taking O(n+r) space and O(r+n2) time, where r is the total number of elements in the set (i,j)|s1[i]=s2[j]. The algorithm can be more efficient than relevant classical algorithms in specific ranges of r.