Genomes present various types of repeated structures having important roles in the mechanism of evolution. In particular, tandem repeats are analysed for their impact on genetic backgrounds of inherited diseases. However, the main objective of today's de novo assemblers is to output long, high-quality, assembled sequences; to this end, they use heuristic-based assembling procedures, which can leave many repeated regions unassembled - and in particular exact tandem repeats - due to the genomes complexity. In this paper, we propose an effective method, called DExTaR, that improves the detection of exact tandem repeats (ETRs) in any de novo de Bruijn assembly. DExTaR is based on a de Bruijn graph constructed by an assembler and retrieves ETRs left unassembled. When used with the well-known assembler ABySS, we show that DExTaR is able to obtain high quality results in terms of number and length of the detected ETRs.

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, É. 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 $\pi$?

MOTIVATION: Modules in biology appeared quickly as an accurate way for summarizing complex living systems by simple ones. Therefore, finding an appropriate relationship between modules extracted from a biological graph and protein complexes remains a crucial task. Recent studies successfully proposed various descriptions of protein interaction networks. These approaches succeed in showing modules within the network and how the modules interact. However, describing the interactions within the modules, i.e. intra-modular interactions, remains little analyzed despite its interest for understanding module functions. RESULTS: We overcome this weakness by adding a complementary description to the already successful approaches: a hierarchical decomposition named homogeneous decomposition. This decomposition represents a natural refinement of previous analyses and details interactions within a module. We propose to illustrate these improvements by three practical cases. Among them, we decompose the yeast protein interaction network and show reachable biological insights that might be extracted from a complex large-scale network. AVAILABILITY: A program is at disposal under CeCILL license at: www.lina.univ-nantes.fr/combi/DH/Home.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.