On a cyclic string-to-string correction problem
Information Processing Letters
Block edit models for approximate string matching
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
On the common substring alignment problem
Journal of Algorithms
The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Edit Distance with Move Operations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
A space-efficient algorithm for sequence alignment with inversions and reversals
Theoretical Computer Science - Special papers from: COCOON 2003
The greedy algorithm for the minimum common string partition problem
ACM Transactions on Algorithms (TALG)
Alignment with non-overlapping inversions in O(n3)-time
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
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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(n3) with a restricted scoring scheme. In this paper, we show that the alignment problem extended to non-overlapping moves can be solved in O(n5) for general scoring schemes, O(n4 log n) for concave scoring schemes and O(n4) for restricted scoring schemes. Furthermore, we show that the alignment problem extended to nonoverlapping 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.