Alignments with Non-overlapping Moves, Inversions and Tandem Duplications in O(n4) Time
Sequence alignment is a central problem in bioinformatics. The classical dynamic programming algorithm aligns two sequences by optimizing over possible insertions, deletions and substitution. 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 4logn) 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.
KeywordsTandem Duplication Edit Operation Edit Graph Grid Graph Alignment Problem
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- 6.Cormode, G., Muthukrishnan, S.: The string edit distance matching problem with moves. In: SODA 2002. Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA. Society for Industrial and Applied Mathematics, pp. 667–676. ACM Press, New York (2002)Google Scholar
- 8.Schoeninger, M., Waterman, M.S.: A local algorithm for dna sequence alignment with inversions. Bull. Math. Biol. 54(4), 521–536 (1992)Google Scholar
- 11.Alves, C.E.R., do Lago, A.P., Vellozo, A.F.: Alignment with non-overlapping inversions in o(n 3 logn) time. In: Proceedings of GRACO 2005. Electronic Notes in Discrete Mathematics, vol. 19, pp. 365–371. Elsevier, Amsterdam (2005)Google Scholar
- 22.Myers, E.W.: An overview of sequence comparison algorithms in molecular biology. Technical Report 91-29, Univ. of Arizona, Dept. of Computer Science (1991)Google Scholar
- 23.Gusfield, D.: Algorithms on Strings, Trees, and Sequences: computer science and computational biology. Press Syndicate of the University of Cambridge, Cambridge (1997/1999)Google Scholar
- 28.Monge, G.: Déblai et remblai. Mémoires de l’Académie Royale des Sciences (1781)Google Scholar