An O(n4) algorithm for alignment with non-overlapping inversions

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 kind 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(n) exact solution for the alignment with non-overlapping inversions problem, and introduced a heuristic for it that brings the running-time complexity down. In this paper, n denotes the maximal length of the two aligned sequences. The present paper gives an exact algorithm for the simplified problem. We give a quite simple dynamic program with O(n)-time and O(n)space complexity for alignments with non-overlapping inversions.