Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
A 3/2-approximation algorithm for sorting by reversals
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On the common substring alignment problem
Journal of Algorithms
On the complexity of the Extended String-to-String Correction Problem
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Assignment of Orthologous Genes via Genome Rearrangement
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A space efficient algorithm for sequence alignment with inversions
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Efficient matching of biological sequences allowing for non-overlapping inversions
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Alignments with non-overlapping moves, inversions and tandem duplications in O(n4) time
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Efficient string-matching allowing for non-overlapping inversions
Theoretical Computer Science
Text searching allowing for inversions and translocations of factors
Discrete Applied Mathematics
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Alignments of sequences are widely used for biological sequence comparisons. Only biological events like mutations, insertions and deletions are usually modeled and other biological events like inversions are not automatically detected by the usual alignment algorithms. Alignment with inversions does not have a known polynomial algorithm and a simplification to the problem that considers only non-overlapping inversions were proposed by Schöniger and Waterman [20] in 1992 as well as a corresponding O(n6) solution. An improvement to an algorithm with O(n3 logn)-time complexity was announced in an extended abstract [1] and, in this present paper, we give an algorithm that solves this simplified problem in O(n3)-time and O(n2)-space in the more general framework of an edit graph. Inversions have recently [4,7,13,17] been discovered to be very important in Comparative Genomics and Scherer et al. in 2005 [11] experimentally verified inversions that were found to be polymorphic in the human genome. Moreover, 10% of the 1,576 putative inversions reported overlap RefSeq genes in the human genome. We believe our new algorithms may open the possibility to more detailed studies of inversions on DNA sequences using exact optimization algorithms and we hope this may be particularly interesting if applied to regions around known rearrangements boundaries. Scherer report 29 such cases and prioritize them as candidates for biological and evolutionary studies.