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
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
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
1.375-Approximation Algorithm for Sorting by Reversals
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
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
Multichromosomal Genome Median and Halving Problems
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
A simpler 1.5-approximation algorithm for sorting by transpositions
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Sorting by transpositions is difficult
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The 1.375 approximation algorithm for sorting by transpositions can run in O(n log n) time
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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A cut-and-paste operation can be a reversal, a transposition, or a transreversal on circular or linear permutations. There are several approximation algorithms for sorting signed permutations by combinations of these operations. For sorting unsigned permutations, we only know an algorithm with performance ratio 3 and its improved version with performance ratio 2.8386+@d allowing reversals and transpositions. In this paper, we present a 2.25-approximation algorithm for sorting unsigned circular permutations by cut-and-paste operations. A structure called tie is proposed to represent the alternating path of length 5. We can classify the ties into 6 types and find ways to remove the breakpoints for each type of ties, so that every cut-and-paste operation can reduce at least 43 breakpoints averagely. Our algorithm can be used to sort unsigned linear permutations and achieve the performance ratio 2.25 if another operation named revrev is allowed.