When biologically significant similarities are present in certain parts of
DNA fragments and are not present in others, biologists attempt to maximize
the alignment score s(vi . . . vi0 ,wj . . .wj0 ), over all substrings vi . . . vi0
of v and wj . . .wj0 of w. This is called the Local Alignment problem since the
alignment does not necessarily extend over the entire string length as it does
in the Global Alignment problem.