Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
SIAM Journal on Discrete Mathematics
A 2-approximation algorithm for genome rearrangements by reversals and transpositions
Theoretical Computer Science - Special issue: Genome informatics
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
To cut…or not to cut (applications of comparative physical maps in molecular evolution)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A Faster and Simpler Algorithm for Sorting Signed Permutations by Reversals
SIAM Journal on Computing
Signed genome rearrangement by reversals and transpositions: models and approximations
Theoretical Computer Science
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
(1 + ɛ)-Approximation of sorting by reversals and transpositions
Theoretical Computer Science
1.375-Approximation Algorithm for Sorting by Reversals
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A 1.5-approximation algorithm for sorting by transpositions and transreversals
Journal of Computer and System Sciences - Special issue on bioinformatics II
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Faster algorithms for sorting by transpositions and sorting by block interchanges
ACM Transactions on Algorithms (TALG)
An approximation algorithm for sorting by reversals and transpositions
Journal of Discrete Algorithms
A 2.25-Approximation Algorithm for Cut-and-Paste Sorting of Unsigned Circular Permutations
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Sorting Signed Permutations by Inversions in O(nlogn) Time
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics
A simpler and faster 1.5-approximation algorithm for sorting by transpositions
Information and Computation
Bitonic sort on a chained-cubic tree interconnection network
Journal of Parallel and Distributed Computing
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Reversals, transpositions and transreversals are common events in genome rearrangement. The genome rearrangement sorting problem is to transform one genome into another using the minimum number of given rearrangement operations. An integer permutation is used to represent a genome in many cases. It can be divided into disjoint strips with each strip denoting a block of consecutive integers. A singleton is a strip of one integer. And the genome rearrangement problem turns into the problem of sorting a permutation into the identity permutation equivalently. Hannenhalli and Pevzner designed a polynomial time algorithm for the unsigned reversal sorting problem on those permutations with O(logn) singletons. In this paper, first we describe one case in which Hannenhalli and Pevzner's algorithm may fail and propose a corrected approach. In addition, we propose a (1 + ε)-approximation algorithm for sorting unsigned permutations with O(log n) singletons by reversals of weight 1 and transpositions/transreversals of weight 2.