Two algorithms for LCS Consecutive Suffix Alignment

The problem of aligning two sequences A and B to determine their similarity is one of the fundamental problems in pattern matching. A challenging, basic variation of the sequence similarity problem is the incremental string comparison problem, denoted Consecutive Suffix Alignment, which is, given two strings A and B, to compute the alignment solution of each suffix of A versus B.Here, we present two solutions to the Consecutive Suffix Alignment Problem under the LCS (Longest Common Subsequence) metric, where the LCS metric measures the subsequence of maximal length common to A and B. The first solution is an O(nL) time and space algorithm for constant alphabets, where the size of the compared strings is O(n) and L⩽n denotes the size of the LCS of A and B.The second solution is an O(nL+nlog|Σ|) time and O(n) space algorithm for general alphabets, where Σ denotes the alphabet of the compared strings.