Recently, a new approach to analyze genomes evolving which is based on comparision of gene orders versus traditional comparision of DNA sequences was proposed (Sankoff et al. 1992). The approach is based on the global rearrangements (e.g., inversions and transpositions of fragments). Analysis of genomes evolving by inversions and transpositions leads to a combinatorial problem of sorting by reversals and transpositions, i.e., sorting of a permutation using reversals and transpositions of arbitrary fragments. We study sorting of signed permutations by reversals and transpositions, a problem which adequately models genome rearrangements, as the genes in DNA are oriented. We establish a lower bound and give a 2-approximation algorithm for the problem. © 1999 - Elsevier Science B.V. All rights reserved.
Gu, Q. P., Peng, S., & Sudborough, H. (1999). A 2-approximation algorithm for genome rearrangements by reversals and transpositions. Theoretical Computer Science, 210(2), 327–339. https://doi.org/10.1016/S0304-3975(98)00092-9