Sorting permutations by block-interchanges
Information Processing Letters
SIAM Journal on Discrete Mathematics
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
Discrete Mathematics
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Analysis and implementation of sorting by transpositions using permutation trees
BSB'11 Proceedings of the 6th Brazilian conference on Advances in bioinformatics and computational biology
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Sorting permutations by transpositions is an important and difficult problem in genome rearrangements. The transposition diameter $TD(n)$ is the maximum transposition distance among all pairs of permutations in $S_n$. It was previously conjectured [H. Eriksson et al., Discrete Math., 241 (2001), pp. 289-300] that $TD(n)\leq\lceil\frac{n+1}{2}\rceil$. This conjecture was disproved by Elias and Hartman [IEEE/ACM Trans. Comput. Biol. Bioinform., 3 (2006), pp. 369-379] by showing $TD(n)\geq\lfloor\frac{n+1}{2}\rfloor+1$. In this paper we improved the lower bound to $TD(n)\geq\frac{17}{33}n+\frac{1}{33}$ via computation.