# A sparse dynamic programming algorithm for alignment with non-overlapping inversions

Alair Pereira Do Lago; Ilya Muchnik; Casimir Kulikowski

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

- Volume: 39, Issue: 1, page 175-190
- ISSN: 0988-3754

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topDo Lago, Alair Pereira, Muchnik, Ilya, and Kulikowski, Casimir. "A sparse dynamic programming algorithm for alignment with non-overlapping inversions." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 175-190. <http://eudml.org/doc/245917>.

@article{DoLago2005,

abstract = {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 $O(n^6)$ 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 $O(n^4)$-time and $O(n^2)$-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.},

author = {Do Lago, Alair Pereira, Muchnik, Ilya, Kulikowski, Casimir},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

language = {eng},

number = {1},

pages = {175-190},

publisher = {EDP-Sciences},

title = {A sparse dynamic programming algorithm for alignment with non-overlapping inversions},

url = {http://eudml.org/doc/245917},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Do Lago, Alair Pereira

AU - Muchnik, Ilya

AU - Kulikowski, Casimir

TI - A sparse dynamic programming algorithm for alignment with non-overlapping inversions

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 1

SP - 175

EP - 190

AB - 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 $O(n^6)$ 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 $O(n^4)$-time and $O(n^2)$-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.

LA - eng

UR - http://eudml.org/doc/245917

ER -

## References

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