A 2.25-Approximation Algorithm for Cut-and-Paste Sorting of Unsigned Circular Permutations

Authors:
Xiaowen Lou;Daming Zhu
Affiliations:
School of Computer Science and Technology, Shandong University, Jinan, P.R. China 250101;School of Computer Science and Technology, Shandong University, Jinan, P.R. China 250101
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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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+茂戮驴, 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.