The complexity of finding minimum-length generator sequences
Theoretical Computer Science
A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Sorting permutations by block-interchanges
Information Processing Letters
SIAM Journal on Discrete Mathematics
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
Sorting by Prefix Transpositions
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
New Bounds and Tractable Instances for the Transposition Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Bounding Prefix Transposition Distance for Strings and Permutations
HICSS '08 Proceedings of the Proceedings of the 41st Annual Hawaii International Conference on System Sciences
Algorithmic approaches for genome rearrangement: a review
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Polynomial-time sortable stacks of burnt pancakes
Theoretical Computer Science
Sorting by transpositions is difficult
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The distribution of cycles in breakpoint graphs of signed permutations
Discrete Applied Mathematics
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A number of fields, including genome rearrangements and interconnection network design, are concerned with sorting permutations in "as few moves as possible", using a given set of allowed operations. These often act on just one or two segments of the permutation, e.g. by reversing one segment or exchanging two segments. The cycle graphof the permutation to sort is a fundamental tool in the theory of genome rearrangements. In this paper, we present an algebraic reinterpretation of the cycle graph as an even permutation, and show how to reformulate our sorting problems in terms of particular factorisations of the latter permutation. Using our framework, we recover known results in a simple and unified way, and obtain a new lower bound on the prefix transposition distance(where a prefix transpositiondisplaces the initial segment of a permutation), which is shown to outperform previous results. Moreover, we use our approach to improve the best known lower bound on the prefix transposition diameterfrom 2n/3 to $\left\lfloor\frac{3n+1}{4}\right \rfloor$.