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40
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
Visualizing Related Metabolic Pathways in Two and a Half Dimensions
, 2003
"... We propose a method for visualizing a set of related metabolic pathways using 2 2 D graph drawing. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant di#erences among the pathways. Layouts are ..."
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Cited by 26 (7 self)
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We propose a method for visualizing a set of related metabolic pathways using 2 2 D graph drawing. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant di#erences among the pathways. Layouts are determined by a global layout of the union of all pathwayrepresenting graphs using a variant of the proven Sugiyama approach for layered graph drawing that allows edges to cross if they appear in di#erent graphs.
Towards Constructing Physical Maps by Optical Mapping: An Effective, Simple, Combinatorial Approach (Extended Abstract)
, 1997
"... ) S. Muthukrishnan Laxmi Parida y Abstract We initiate the complexity study of physical mapping with the emerging technology of Optical Mapping (OM) pioneered by the team lead by David Schwartz at the W. M. Keck Laboratory for Biomolecular Imaging, Dept of Chemistry, NYU. In currently popular e ..."
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Cited by 16 (6 self)
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) S. Muthukrishnan Laxmi Parida y Abstract We initiate the complexity study of physical mapping with the emerging technology of Optical Mapping (OM) pioneered by the team lead by David Schwartz at the W. M. Keck Laboratory for Biomolecular Imaging, Dept of Chemistry, NYU. In currently popular electrophoretic approaches, information about the relative ordering of the fragments comprising the DNA molecule is lost, thus leading to difficult computational problems of composing the fragments in to a physical map depicting their relative order. In contrast, the relative ordering of the pieces is readily obtained in OM. However, OM faces serious technological challenges as it has low resolution and is faultprone. We take a combinatorial approach to the problem of constructing physical maps from the erroneous data generated by OM. We identify two abstract problems in this context, namely, the Exclusive Binary FlipCut and Exclusive Weighted FlipCut problems. For both, we present polynom...
A BranchandCut Approach to Physical Mapping of Chromosomes By Unique EndProbes
, 1997
"... A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 5276, 1995) first considered ..."
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Cited by 15 (5 self)
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A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 5276, 1995) first considered a maximumlikelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics. We show that by exploiting information about the endprobes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the welldeveloped tools of integer linearprogramming and branchandcut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness...
Visual understanding of metabolic pathways across organisms using layout in two and a half dimensions
 JOURNAL OF INTEGRATIVE BIOINFORMATICS
, 2004
"... We propose a method for visualizing a set of related metabolic pathways across organisms using 2 1/2 dimensional graph visualization. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant differences am ..."
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Cited by 13 (8 self)
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We propose a method for visualizing a set of related metabolic pathways across organisms using 2 1/2 dimensional graph visualization. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant differences among the pathways. The (dis)similarities between pathways are expressed by the Hamming distances of the underlying graphs which are used to compute a stacking order for the pathways. Layouts are determined by a global layout of the union of all pathway graphs using a variant of the proven Sugiyama approach for layered graph drawing. Our variant layout approach allows edges to cross if they appear in different graphs.
Algorithms for Computing and Integrating Physical Maps Using Unique Probes
 PROCEEDINGS OF THE 1ST ACM CONFERENCE ON COMPUTATIONAL MOLECULAR BIOLOGY
, 1997
"... Current physical mapping projects based on STSprobes involve additional clues such as the fact that some probes are anchored to a known map and that others come from the ends of clones. Because of the disparate combinatorial contributions of these varied data items, it is difficult to design a "tai ..."
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Cited by 12 (0 self)
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Current physical mapping projects based on STSprobes involve additional clues such as the fact that some probes are anchored to a known map and that others come from the ends of clones. Because of the disparate combinatorial contributions of these varied data items, it is difficult to design a "tailored" algorithm that incorporates them all. Moreover, it is inevitable that new experiments will provide new kinds of data, making obsolete any such algorithm. We show how to convert the physical mapping problem into a 0/1 linear programming (LP) problem. We further show how one can incorporate additional clues as additional constraints in the LP formulation. We give a simple relaxation of the 0/1 LP problem that solves problems of the same scale as previously reported tailored algorithms to equal or greater optimization levels. We also present a theorem proving that when the data is 100% accurate, then the relaxed and integer solutions coincide. The LP algorithm suffices to solve problems ...
An Optimal Procedure for Gap Closing in Whole Genome Shotgun Sequencing
, 2001
"... Tettelin et. al. proposed a new method for closing the gaps in whole genome shotgun sequencing projects. The method uses a multiplex PCR strategy in order to minimize the time and eort required to sequence the DNA in the missing gaps. This procedure has been used in a number of microbial seque ..."
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Cited by 12 (3 self)
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Tettelin et. al. proposed a new method for closing the gaps in whole genome shotgun sequencing projects. The method uses a multiplex PCR strategy in order to minimize the time and eort required to sequence the DNA in the missing gaps. This procedure has been used in a number of microbial sequencing projects including Streptococcus pneumoniae and other bacteria. In this paper we describe a theoretical framework for this problem and propose an improved method that guarantees Address: Dept. of Computer and Information Sciences, Wachman Hall Rm 304 (03824), Temple University, 1805 N Broad St, Philadelphia PA 191226094, USA. Research performed in part at DIMACS. Email: beigel@joda.cis.temple.edu. Supported in part by the National Science Foundation under grants CCR9996021, and CCR0049019. y Address: Dept. of Mathematics, Tel Aviv University, 69978 Tel Aviv, ISRAEL. Email: noga@math.tau.ac.il. z Email: apaydin@cs.stanford.edu. x Address: 4 Independence Way, Pri...
The consecutive ones submatrix problem for sparse matrices
 Algorithmica
, 2004
"... A 01 matrix has the Consecutive Ones Property (C1P) if there is a permutation of its columns that leaves the 1’s consecutive in each row. The Consecutive Ones Submatrix (C1S) problem is, given a 01 matrix A, to find the largest number of columns of A that form a submatrix with the C1P property. Su ..."
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Cited by 11 (0 self)
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A 01 matrix has the Consecutive Ones Property (C1P) if there is a permutation of its columns that leaves the 1’s consecutive in each row. The Consecutive Ones Submatrix (C1S) problem is, given a 01 matrix A, to find the largest number of columns of A that form a submatrix with the C1P property. Such a problem finds application in physical mapping with hybridization data in genome sequencing. Let (a, b)matrices be the 01 matrices in which there are at most a 1’s in each column and at most b 1’s in each row. This paper proves that the C1S problem remains NPhard for i) (2, 3)matrices and ii) (3, 2)matrices. This solves an open problem posed in a recent paper of Hajiaghayi and Ganjali [1]. We further prove that the C1S problem is polynomialtime 0.8approximatable for (2, 3)matrices in which no two columns are identical and 0.5approximatable for (2, ∞)matrices in general. we also show that the C1S problem is polynomialtime 0.5approximatable for (3, 2)matrices. However, there exists an ɛ> 0 such that approximating the C1S problem for (∞, 2)matrices within a factor of n ɛ (where n is the number of columns of the input matrix) is NPhard. Keywords: NPhardness, approximation algorithm, consecutive ones property, consecutive ones submatrix, caterpillar spanning tree 1
A BranchandCut Approach to Physical Mapping With EndProbes
, 1997
"... A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig [AKWZ94] first considered a maximumlikelihood model o ..."
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Cited by 10 (0 self)
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A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig [AKWZ94] first considered a maximumlikelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics. We show that by exploiting information about the endprobes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the welldeveloped tools of integer linearprogramming and branchandcut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively...
Minimal Conflicting Sets for the Consecutive Ones Property in ancestral genome reconstruction
, 912
"... Abstract. A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1’s on each row are consecutive. A Minimal Conflicting Set is a set of rows that does not have the C1P, but every proper subset has the C1P. Such submatrices have been considered in ..."
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Cited by 9 (4 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 1’s on each row are consecutive. A Minimal Conflicting Set is a set of rows that does not have the C1P, but every proper subset has the C1P. Such submatrices have been considered in comparative genomics applications, but very little is known about their combinatorial structure and efficient algorithms to compute them. We first describe an algorithm that detects rows that belong to Minimal Conflicting Sets. This algorithm has a polynomial time complexity when the number of 1s in each row of the considered matrix is bounded by a constant. Next, we show that the problem of computing all Minimal Conflicting Sets can be reduced to the joint generation of all minimal true clauses and maximal false clauses for some monotone boolean function. We use these methods on simulated data related to ancestral genome reconstruction to show that computing Minimal Conflicting Set is useful in discriminating between true positive and false positive ancestral syntenies. We also study a dataset of yeast genomes and address the reliability of an ancestral genome proposal of the Saccahromycetaceae yeasts. Draft, do not distribute. Version of December 21, 2009. 1