A Simpler 1.5-Approximation Algorithm for Sorting by Transpositions

Abstract

AbstractAn important problem in genome rearrangements is sorting permutations by transpositions. Its complexity is still open, and two rather complicated 1.5-approximation algorithms for sorting linear permutations are known (Bafna and Pevzner, 96 and Christie, 98). In this paper, we observe that the problem of sorting circular permutations by transpositions is equivalent to the problem of sorting linear permutations by transpositions. Hence, all algorithms for sorting linear permutations by transpositions can be used to sort circular permutations. Our main result is a new 1.5-approximation algorithm, which is considerably simpler than the previous ones, and achieves running time which is equal to the best known. Moreover, the analysis of the algorithm is significantly less involved, and provides a good starting point for studying related open problems.KeywordsGenome RearrangementCircular PermutationIdentity PermutationOriented CycleBlack EdgeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.