Alignments with non-overlapping moves, inversions and tandem duplications in O ( n 4 ) time

Sequence alignment is a central problem in bioinformatics. The classical dynamic programming algorithm aligns two sequences by optimizing over possible insertions, deletions and substitutions. However, other evolutionary events can be observed, such as inversions, tandem duplications or moves (transpositions). It has been established that the extension of the problem to move operations is NP-complete. Previous work has shown that an extension restricted to non-overlapping inversions can be solved in O ( n 3 ) with a restricted scoring scheme. In this paper, we show that the alignment problem extended to non-overlapping moves can be solved in O ( n 5 ) for general scoring schemes, O ( n 4 log n ) for concave scoring schemes and O ( n 4 ) for restricted scoring schemes. Furthermore, we show that the alignment problem extended to non-overlapping moves, inversions and tandem duplications can be solved with the same time complexities. Finally, an example of an alignment with non-overlapping moves is provided.