A simpler and faster 1.5-approximation algorithm for sorting by transpositions

TLDR: All algorithms for sorting linear permutations by transpositions can be used to sort circular permutations, and a new O(n 3/2 log n) 1.5-approximation algorithm is observed, which is considerably simpler than previously reported.

Abstract: An important problem in genome rearrangements is sorting permutations by transpositions. The complexity of the problem is still open, and two rather complicated 1.5-approximation algorithms for sorting linear permutations are known (Bafna and Pevzner, 98 and Christie, 99). The fastest known algorithm is the quadratic algorithm of Bafna and Pevzner. 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 O(n3/2√log n) 1.5-approximation algorithm, which is considerably simpler than the previous ones, and whose analysis is significantly less involved.