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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 28 (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 10 (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.
Approximability and parameterized complexity of consecutive ones submatrix problems
 IN PROC. 4TH TAMC, VOLUME 4484 OF LNCS
, 2007
"... We develop a refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This novel characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the problem to find a maximum ..."
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Cited by 8 (4 self)
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We develop a refinement of a forbidden submatrix characterization of 0/1matrices fulfilling the Consecutive Ones Property (C1P). This novel characterization finds applications in new polynomialtime approximation algorithms and fixedparameter tractability results for the problem to find a maximumsize submatrix of a 0/1matrix such that the submatrix has the C1P. Moreover, we achieve a problem kernelization based on simple data reduction rules and provide several search tree algorithms. Finally, we derive inapproximability results.
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 8 (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.
A faster algorithm for finding minimum Tucker submatrices
"... 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. ..."
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Cited by 2 (1 self)
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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 ∆ 1entries per row, thereby improving the O( ∆ 3 m 2 (mn + n 3)) time algorithm of Dom et al. [17]. 1
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.
Selectivity Estimation of Twig Queries on Cyclic Graphs
"... Abstract—Recent applications including the Semantic Web, Web ontology and XML have sparked a renewed interest on graphstructured databases. Among others, twig queries have been a popular tool for retrieving subgraphs from graphstructured databases. To optimize twig queries, selectivity estimation h ..."
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Abstract—Recent applications including the Semantic Web, Web ontology and XML have sparked a renewed interest on graphstructured databases. Among others, twig queries have been a popular tool for retrieving subgraphs from graphstructured databases. To optimize twig queries, selectivity estimation has been a crucial and classical step. However, the majority of existing works on selectivity estimation focuses on relational and tree data. In this paper, we investigate selectivity estimation of twig queries on possibly cyclic graph data. To facilitate selectivity estimation on cyclic graphs, we propose a matrix representation of graphs derived from prime labeling — a scheme for reachability queries on directed acyclic graphs. With this representation, we exploit the consecutive ones property (C1P) of matrices. As a consequence, a node is mapped to a point in a twodimensional space whereas a query is mapped to multiple points. We adopt histograms for scalable selectivity estimation. We perform an extensive experimental evaluation on the proposed technique and show that our technique controls the estimationerrorunder1.3%on XMARK and DBLP,whichismore accurate than previous techniques. On TREEBANK, we produce RMSE and NRMSE 6.8 times smaller than previous techniques. I.
Variants of the ConsecutiveOnes Property Motivated by the Reconstruction of Ancestral Species
, 2012
"... The polynomialtime decidable ConsecutiveOnes Property (C1P) of binary matrices, formally introduced in 1965 by Fulkerson and Gross [52], has since found applications in many areas. In this thesis, we propose and study several variants of this property that are motivated by the reconstruction of an ..."
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The polynomialtime decidable ConsecutiveOnes Property (C1P) of binary matrices, formally introduced in 1965 by Fulkerson and Gross [52], has since found applications in many areas. In this thesis, we propose and study several variants of this property that are motivated by the reconstruction of ancestral species. We first propose the Gapped C1P, or the (k,δ)ConsecutiveOnes Property ((k,δ)C1P): a binary matrix M has the (k,δ)C1P for integers k and δ if the columns of M can be permuted such that each row contains at most k blocks of1’s and no two neighboring blocks of 1’s are separated by a gap of more than δ 0’s. The C1P is equivalent to the (1,0)C1P. We show that for every bounded and unbounded k ≥ 2,δ ≥ 1,(k,δ)̸=(2,1), deciding the(k,δ)C1P is NPcomplete [55]. We also provide an algorithm for a relevant case of the (2,1)C1P. We then study the(k,δ)C1P with a bound d on the maximum number of1’s in any row (the maximum degree) of M. We show that the(d,k,δ)ConsecutiveOnes Property ((d,k,δ)C1P) is polynomialtime decidable when all three parameters are fixed constants. Since fixing d also fixes k(k≤d), the only case left to consider