Fully incremental LCS computation

Sequence comparison is & 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.