A 2.25-approximation algorithm for cut-and-paste sorting of unsigned circular permutations

Abstract

We consider sorting unsigned circular permutations by cut-and-paste operations. For a circular permutation, a cut-and-paste operation can be a reversal, a transposition, or a transreversal. For the sorting of signed permutations, there are several approximation algorithms allowing various combinations of these operations. For the sorting of unsigned permutations, we only know a 3-approximation algorithm and an improved algorithm with ratio 2.8386+δ, both allowing reversals and transpositions. In this paper, by new observations on the breakpoint graph, we present a 2.25-approximation algorithm for cut-and-paste sorting of unsigned circular permutations. © 2008 Springer-Verlag Berlin Heidelberg.