Luis Antonio Brasil Kowada

Unitary Toric Classes, the Reality and Desire Diagram, and Sorting by Transpositions

H. Eriksson et al. made a breakthrough to the problem of sorting by transpositions by proposing a quotient structure named toric graph, which allowed the reduction of the search space, establishing the transposition diameter

New Genome Similarity Measures based on Conserved Gene Adjacencies

D_t(n)=\lfloor\frac{n+1}{2}\rfloor+1

Bounds on the transposition distance for lonely permutations

, for the cases

On the Toric Graph as a Tool to Handle the Problem of Sorting by Transpositions

n=13

New Genome Similarity Measures Based on Conserved Gene Adjacencies

and

On the 1.375-Approximation Algorithm for Sorting by Transpositions in O(n logn) Time

n=15

Transposition Diameter and Lonely Permutations

, and invalidating a conjecture by J. Meidanis, M. E. M. T. Walter, and Z. Dias that the transposition diameter would be equal to the transposition distance of the reverse permutation

Analysis and implementation of sorting by transpositions using permutation trees

\lfloor n/2\rfloor+1

A NEW QUANTUM ALGORITHM FOR SOLVING THE MINIMUM SEARCHING PROBLEM

. I. Elias and T. Hartman extended the lower bound

A new reversible circuit synthesis algorithm based on cycle representations of permutations

D_t(n)\geq\lfloor\frac{n+1}{2}\rfloor+1