Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
A Faster and Simpler Algorithm for Sorting Signed Permutations by Reversals
SIAM Journal on Computing
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Advances on sorting by reversals
Discrete Applied Mathematics
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The problem of Sorting signed permutations by reversals is a well studied problem in computational biology. The first polynomial time algorithm was presented by Hannenhalli and Pevzner in 1995 [5]. The algorithm was improved several times, and nowadays the most efficient algorithm has a subquadratic running time [9,8]. Simple permutations played an important role in the development of these algorithms. Although the latest result of Tannier et al. [8] does not require simple permutations the preliminary version of their algorithm [9] as well as the first polynomial time algorithm of Hannenhalli and Pevzner [5] use the structure of simple permutations. However, the latter algorithms require a precomputation that transforms a permutation into an equivalent simple permutation. To the best of our knowledge, all published algorithms for this transformation have at least a quadratic running time. For further investigations on genome rearrangement problems, the existence of a fast algorithm for the transformation could be crucial. In this paper, we present a linear time algorithm for the transformation.