Minimal Conflicting Sets for the Consecutive Ones Property in Ancestral Genome Reconstruction

Chauve, Cédric; Haus, Utz-Uwe; Stephen, Tamon; You, Vivija P.

doi:10.1007/978-3-642-04744-2_5

Cited by 8 publications

(1 citation statement)

References 24 publications

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“…The more conflict there is, the lower proportion of ancestral syntenies kept, and the more arbitrary choices among optimal solutions make big differences on the final result. Preliminary results on conflicts and maximal solutions for the Consecutive Ones Property might be useful in order to better understand this issue (Chauve et al, 2009). …”

Section: Chauve Et Almentioning

confidence: 98%

Yeast Ancestral Genome Reconstructions: The Possibilities of Computational Methods II

Chauve

Gavranović

Ouangraoua

et al. 2010

Journal of Computational Biology

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Since the availability of assembled eukaryotic genomes, the first one being a budding yeast, many computational methods for the reconstruction of ancestral karyotypes and gene orders have been developed. The difficulty has always been to assess their reliability, since we often miss a good knowledge of the true ancestral genomes to compare their results to, as well as a good knowledge of the evolutionary mechanisms to test them on realistic simulated data. In this study, we propose some measures of reliability of several kinds of methods, and apply them to infer and analyse the architectures of two ancestral yeast genomes, based on the sequence of seven assembled extant ones. The pre-duplication common ancestor of S. cerevisiae and C. glabrata has been inferred manually by Gordon et al. (Plos Genet. 2009). We show why, in this case, a good convergence of the methods is explained by some properties of the data, and why results are reliable. In another study, Jean et al. (J. Comput Biol. 2009) proposed an ancestral architecture of the last common ancestor of S. kluyveri, K. thermotolerans, K. lactis, A. gossypii, and Z. rouxii inferred by a computational method. In this case, we show that the dataset does not seem to contain enough information to infer a reliable architecture, and we construct a higher resolution dataset which gives a good reliability on a new ancestral configuration.

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Section: Chauve Et Almentioning

confidence: 98%

Yeast Ancestral Genome Reconstructions: The Possibilities of Computational Methods II

Chauve

Gavranović

Ouangraoua

et al. 2010

Journal of Computational Biology

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A Faster Algorithm for Finding Minimum Tucker Submatrices

Blin

Rizzi

2010

Programs, Proofs, Processes

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Abstract. A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1s on each row are consecutive. Algorithmic issues of the C1P are central in computational molecular biology, in particular for physical mapping and ancestral genome reconstruction. In 1972, Tucker gave a characterization of matrices that have the C1P by a set of forbidden submatrices, and a substantial amount of research has been devoted to the problem of efficiently finding such a minimum size forbidden submatrix. This paper presents a new O(∆ 3 m 2 (m∆ + n 3 )) time algorithm for this particular task for a m × n binary matrix with at most ∆ 1-entries per row, thereby improving the O(∆ 3 m 2 (mn + n 3 )) time algorithm of Dom et al. [17].

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The Complexity of the Gapped Consecutive-Ones Property Problem for Matrices of Bounded Maximum Degree

Maňuch

Patterson

2010

Comparative Genomics

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The Gapped Consecutive-Ones Property (C1P) Problem, or the (k, d)-C1P Problem is: given a binary matrix M and integers k and d, decide if the columns of M can be ordered such that each row contains at most k blocks of 1's, and no two neighboring blocks of 1's are separated by a gap of more than d 0's. This problem was introduced by Chauve et al. (2009b). The classical polynomial-time solvable C1P Problem is equivalent to the (1, 0)-C1P problem. It has been shown that, for every unbounded or bounded k ! 2 and unbounded or bounded d ! 1, except when (k, d) = (2, 1), the (k, d)-C1P Problem is NP-complete (Maň uch et al., 2011;Goldberg et al., 1995). In this article, we study the Gapped C1P Problem with a third parameter d, namely the bound on the maximum number of 1's in any row of M, or the bound on the maximum degree of M. This is motivated by the reconstruction of ancestral genomes (Ma et al., 2006;Chauve and Tannier, 2008), where, in binary matrices obtained from the experiments of Chauve and Tannier (2008), we have observed that the majority of the rows have low degree, while each high degree row contains many rows of low degree. The (d, k, d)-C1P Problem has been shown to be polynomial-time solvable when all three parameters are fixed (Chauve et al., 2009b). Since fixing d also fixes k (k d), the only case left to consider is the case when d is unbounded, or the (d, k, ')-C1P Problem. Here we show that for every d > k ! 2, the (d, k, ')-C1P Problem is NP-complete.

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Minimal Conflicting Sets for the Consecutive Ones Property in Ancestral Genome Reconstruction

Cited by 8 publications

References 24 publications

Yeast Ancestral Genome Reconstructions: The Possibilities of Computational Methods II

Yeast Ancestral Genome Reconstructions: The Possibilities of Computational Methods II

A Faster Algorithm for Finding Minimum Tucker Submatrices

The Complexity of the Gapped Consecutive-Ones Property Problem for Matrices of Bounded Maximum Degree

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