Sorting the Reverse Permutation by Prefix Transpositions

Dias and Meidanis (3) presented, without a proof, an algorithm to sort the reverse permutation Rn = (n, n − 1, . . . ,1) by prefix transpositions. In this report we present a new algorithm based on the previous one and show a complete formal proof of its correctness. From this result we establish a new proved upper bound of n − ⌊n/4⌋ for the prefix transposition distance of Rn.