  Multiple sequence alignment (MSA) has been one of the most important problems
in bioinformatics for more decades and it is still heavily examined by many
mathematicians and biologists. However, mostly because of the practical
motivation of this problem, the research on this topic is focused on aligning
long sequences. It is understandable, since the sequences that need to be
aligned (usually DNA or protein sequences) are generally quite long (e. g., at
least 30-40 characters). Nevertheless, it is a challenging question that
exactly where MSA starts to become a real hard problem (since it is known that
MSA is NP-complete [2]), and the key to answer this question is to examine
short sequences. If the optimal alignment for short sequences could be
determined in polynomial time, then these results may help to develop faster or
more accurate heuristic algorithms for aligning long sequences. In this work,
it is shown that for length-1 sequences using arbitrary metric, as well as for
length-2 sequences using unit metric, the optimum of the MSA problem can be
achieved by the trivial alignment.
