Sorting by transpositions: dealing with length-weighted models

Authors:
Xingqin Qi;Jichang Wu;Shuguang Li;Guojun Li
Affiliations:
Department of Applied Mathematics, Shandong University at Weihai, Weihai 264209, China.;School of Mathematics and System Sciences, Shandong University, Jinan 250100, China.;School of Information and Electronics Engineering, Shandong Institute of Business and Technology, Yantai 264005, China.;School of Mathematics and System Sciences, Shandong University, Jinan 250100, China/ Department of Biochemistry and Molecular Biology, University of Georgia, Athens, Georgia 30602, USA
Venue:
International Journal of Bioinformatics Research and Applications
Year:
2008

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Abstract

For the first time, we study the sorting of permutations bylength-weighted transpositions under a wide class of costfunctions, namely f(l)=lα, where l is the lengthof the transposition. For different α, we give correspondingupper and lower bounds of the cost of sorting any binary sequencesor any permutations. Furthermore, an O(log n) approximationalgorithm and an exact algorithm are given to determine the optimaltransposition series of sorting a permutation of length n when 1