Improved upper bound for sorting permutations by prefix transpositions

Abstract

Modelling of chromosomes with permutations has triggered the research of sorting permutations using global rearrangement operations in computational molecular biology. One such rearrangement is transposition which swaps two adjacent substrings. If one of the substrings is restricted to be the prefix of the permutation then that operation is called a prefix transposition. The symmetric prefix transposition distance between two permutations is defined to be the minimum number of prefix transpositions required to transform one into another. Group theory dictates that an upper bound for prefix transposition distance between any pair of permutations in the symmetric group Sn is equivalent to the upper bound for sorting any permutation with prefix transpositions. In this paper, we improve the upper bound for sorting permutations with prefix transpositions to n−log2⁡n.