Alignment of sequences is widely used for biological sequence
comparisons, and only biological events like mutations, insertions
and deletions are considered. Other biological events like
inversions are not automatically detected by the usual alignment
algorithms, thus some alternative approaches have been tried in order
to include inversions or other kinds of rearrangements.
Despite many important results in the last decade, the complexity of the
problem of alignment with inversions is still unknown. In 1992, Schöniger
and Waterman proposed the simplification hypothesis that the inversions do
not overlap. They also presented an O(n6) exact solution for
the alignment with non-overlapping inversions problem and introduced a
heuristic for it that brings the average case complexity down. (In this work, n is the maximal
length of both sequences that are aligned.)
The present paper gives two exact algorithms for the simplified
problem. We give a quite simple dynamic program with O(n4)-time
and O(n2)-space complexity for alignments with non-overlapping
inversions and exhibit a sparse and exact implementation version of
this procedure that uses much less resources for some applications
with real data.