On Sorting of Signed Permutations by Prefix and Suffix Reversals and Transpositions

A reversal inverts a segment and the signs of the elements of this segment in a permutation. A transposition exchanges the position of two consecutive segments. These are the most common kinds of genome rearrangements. In this paper, we introduce the study of prefix and suffix versions of these operations, that is, when only segments of the beginning or of the end are involved, when considering signed permutations. We gave asymptotic approximation algorithms of factor two for three new problems: when prefix and suffix reversals are allowed, when prefix reversals and prefix transpositions are allowed, and when prefix and suffix reversals and prefix and suffix transpositions are allowed.