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A methodological framework for the reconstruction of contiguous regions of ancestral genomes and its application to mammalian genome
 PLoS Comput. Biol
, 1000
"... The reconstruction of ancestral genome architectures and gene orders from homologies between extant species is a longstanding problem, considered by both cytogeneticists and bioinformaticians. A comparison of the two approaches was recently investigated and discussed in a series of papers, sometimes ..."
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Cited by 27 (13 self)
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The reconstruction of ancestral genome architectures and gene orders from homologies between extant species is a longstanding problem, considered by both cytogeneticists and bioinformaticians. A comparison of the two approaches was recently investigated and discussed in a series of papers, sometimes with diverging points of view regarding the performance of these two approaches. We describe a general methodological framework for reconstructing ancestral genome segments from conserved syntenies in extant genomes. We show that this problem, from a computational point of view, is naturally related to physical mapping of chromosomes and benefits from using combinatorial tools developed in this scope. We develop this framework into a new reconstruction method considering conserved gene clusters with similar gene content, mimicking principles used in most cytogenetic studies, although on a different kind of data. We implement and apply it to datasets of mammalian genomes. We perform intensive theoretical and experimental comparisons with other bioinformatics methods for ancestral genome segments reconstruction. We show that the method that we propose is stable and reliable: it gives convergent results using several kinds of data at different levels of resolution, and all predicted ancestral regions are well supported. The results come eventually very close to cytogenetics studies. It suggests that the comparison of methods for ancestral genome reconstruction should include the algorithmic aspects of the methods as well
Approximation and FixedParameter Algorithms for Consecutive Ones Submatrix Problems
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
"... We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the NPhard ..."
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Cited by 9 (0 self)
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We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the NPhard problem to delete a minimum number of rows or columns from a 0/1matrix such that the remaining submatrix has the C1P.
Algorithmic Aspects of the ConsecutiveOnes Property
, 2009
"... We survey the consecutiveones property of binary matrices. Herein, a binary matrix has the consecutiveones property (C1P) if there is a permutation of its columns that places the 1s consecutively in every row. We provide an overview over connections to graph theory, characterizations, recognition ..."
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Cited by 7 (1 self)
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We survey the consecutiveones property of binary matrices. Herein, a binary matrix has the consecutiveones property (C1P) if there is a permutation of its columns that places the 1s consecutively in every row. We provide an overview over connections to graph theory, characterizations, recognition algorithms, and applications such as integer linear programming and solving Set Cover.
RedBlue Covering Problems and the Consecutive Ones Property
, 2007
"... Set Cover problems are of core importance in many applications. In recent research, the “redblue variants” where blue elements all need to be covered whereas red elements add further constraints on the optimality of a covering have received considerable interest. Application scenarios range from da ..."
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Cited by 1 (1 self)
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Set Cover problems are of core importance in many applications. In recent research, the “redblue variants” where blue elements all need to be covered whereas red elements add further constraints on the optimality of a covering have received considerable interest. Application scenarios range from data mining to interference reduction in cellular networks. As a rule, these problem variants are computationally at least as hard as the original set cover problem. In this work we investigate whether and how the wellknown consecutive ones property, restricting the structure of the input sets, makes the redblue covering problems feasible. We explore a sharp border between polynomialtime solvability and NPhardness for these problems.
Hardness Results for the Gapped ConsecutiveOnes Property Problem
, 2009
"... Motivated by problems of comparative genomics and paleogenomics, in [6] the authors introduced the Gapped ConsecutiveOnes Property Problem (k, δ)C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k blocks of ones and no two ..."
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Cited by 1 (1 self)
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Motivated by problems of comparative genomics and paleogenomics, in [6] the authors introduced the Gapped ConsecutiveOnes Property Problem (k, δ)C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k blocks of ones and no two consecutive blocks of ones are separated by a gap of more than δ zeros. The classical C1P problem, which is known to be polynomial is equivalent to the (1, 0)C1P problem. They showed that the (2, δ)C1P Problem is NPcomplete for all δ ≥ 2 and that the (3, 1)C1P problem is NPcomplete. They also conjectured that the (k, δ)C1P Problem is NPcomplete for k ≥ 2, δ ≥ 1 and (k, δ)̸ = (2,1). Here, we prove that this conjecture is true. The only remaining case is the (2,1)C1P Problem, which could be polynomialtime solvable.
On the Gapped Consecutive Ones Property
"... Abstract. Motivated by problems of comparative genomics and paleogenomics, we introduce the Gapped ConsecutiveOnes Property Problem (k,δ)C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k sequences of 1’s and no two consecu ..."
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Cited by 1 (0 self)
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Abstract. Motivated by problems of comparative genomics and paleogenomics, we introduce the Gapped ConsecutiveOnes Property Problem (k,δ)C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k sequences of 1’s and no two consecutive sequences of 1’s are separated by a gap of more than δ 0’s. The classical C1P problem, which is known to be polynomial, is equivalent to the (1,0)C1P Problem. We show that the (2,δ)C1P Problem is NPcomplete for δ ≥ 2. We conjecture that the (k, δ)C1P Problem is NPcomplete for k ≥ 2, δ ≥ 1, (k, δ) ̸ = (2, 1). We also show that the (k,δ)C1P problem can be reduced to a graph bandwidth problem parameterized by a function of k, δ and of the maximum number s of 1’s in a row of M, and hence is polytime solvable if all three parameters are constant.
On matrices that do not . . .
, 2009
"... A binary matrix has the consecutive ones property if its columns can be ordered in such a way that, in each row, all 1s are consecutive. This classical combinatorial notion has been central in genomic problems such as physical mapping or paleogenomics. In these fields, genomes that cannot be sequenc ..."
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A binary matrix has the consecutive ones property if its columns can be ordered in such a way that, in each row, all 1s are consecutive. This classical combinatorial notion has been central in genomic problems such as physical mapping or paleogenomics. In these fields, genomes that cannot be sequenced are represented by a matrix that has the consecutive ones property, but are inferred from an initial matrix that does not have this property due to errors. In this work, we study combinatorial and algorithmic characterizations of matrices that do not have the consecutive ones property. We review existing results and propose new results centered around the notion of minimal conflicting sets.