SORTING BY TRANSPOSITIONS IS DIFFICULT

作者：Bulteau Laurent^*; Fertin Guillaume; Rusu Irena

来源：SIAM Journal on Discrete Mathematics, 2012, 26(3): 1148-1180.

DOI：10.1137/110851390

• theoretical aspects of computational biology
• comparative genomics
• transposition distance
• computational complexity

In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance between two genomes, that is, the minimum number of transpositions needed to transform a genome into another, is, according to numerous studies, a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations is called the Sorting by Transpositions problem, and has been introduced by Bafna and Pevzner in [Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, 1995, pp. 614-623]. It has naturally been the focus of a number of studies (see, for instance, [G. Fertin, A. Labarre, I. Rusu, E.Tannier, and S. Vialette, Combinatorics of Genome Rearrangements, The MIT Press, Cambridge, MA, 2009]), but the computational complexity of this problem has remained undetermined for 15 years. In this paper, we answer this long-standing open question by proving that the Sorting by Transpositions problem is NP-hard. As a corollary of our result, we also prove that the following problem, first described in [D. A. Christie, Genome Rearrangement Problems, Ph.D. thesis, University of Glasgow, Glasgow, Scotland, 1998], is NP-hard: given a permutation pi, is it possible to sort p using exactly d(b)(pi)/3 transpositions, where d(b)(pi) is the number of breakpoints of pi?

• 出版日期2012