Sorting by Transpositions Is Difficult

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 releva...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on discrete mathematics Vol. 26; no. 3; pp. 1148 - 1180
Main Authors Bulteau, Laurent, Fertin, Guillaume, Rusu, Irena
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Subjects
Algorithms
Approximation
Bioinformatics
Computational Complexity
Computer Science
Genomes
Genomics
Life Sciences
Quantitative Methods
Theoretical Aspects of Computational Biology
Transposition Distance
Comparative Genomics
Computational Complexity
Online AccessGet full text

Cover

More Information
Summary: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 \sf 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 \sf NP-hard: given a permutation $\pi$, is it possible to sort $\pi$ using exactly $d_b(\pi)/3$ transpositions, where $d_b(\pi)$ is the number of breakpoints of $\pi$? [PUBLICATION ABSTRACT]
ISSN:0895-4801
1095-7146
DOI:10.1137/110851390