  The nature of the alignment with gaps corresponding to a longest common
subsequence (LCS) of two independent iid random sequences drawn from a finite
alphabet is investigated. It is shown that such an optimal alignment typically
matches pieces of similar short-length. This is of importance in understanding
the structure of optimal alignments of two sequences. Moreover, it is also
shown that any property, common to two subsequences, typically holds in most
parts of the optimal alignment whenever this same property holds, with high
probability, for strings of similar short-length. Our results should, in
particular, prove useful for simulations since they imply that the re-scaled
two dimensional representation of a LCS gets uniformly close to the diagonal as
the length of the sequences grows without bound.
