The simplest form of a sequence similarity analysis is the Longest Common
Subsequence (LCS) problem, where we eliminate the operation of substitution
and allow only insertions and deletions. A subsequence of a string v
is simply an (ordered) sequence of characters (not necessarily consecutive)
from v. For example, if v = ATTGCTA, then AGCA and ATTA are subsequences
of v whereas TGTT and TCG are not.9 A common subsequence of
two strings is a subsequence of both of them. Formally, we define the com-
mon subsequence of strings v = v1 . . . vn and w = w1 . . .wm as a sequence of
positions in v,