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Maximum Likelihood Genome Assembly
, 2009
"... Whole genome shotgun assembly is the process of taking many short sequenced segments (reads) and reconstructing the genome from which they originated. We demonstrate how the technique of bidirected network flow can be used to explicitly model the doublestranded nature of DNA for genome assembly. By ..."
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Whole genome shotgun assembly is the process of taking many short sequenced segments (reads) and reconstructing the genome from which they originated. We demonstrate how the technique of bidirected network flow can be used to explicitly model the doublestranded nature of DNA for genome assembly. By combining an algorithm for the Chinese Postman Problem on bidirected graphs with the construction of a bidirected de Bruijn graph, we are able to find the shortest doublestranded DNA sequence that contains a given set of klong DNAmolecules. This is the first exact polynomial time algorithm for the assembly of a doublestranded genome. Furthermore, we propose a maximum likelihood framework for assembling the genome that is the most likely source of the reads, in lieu of the standard maximum parsimony approach (which finds the shortest genome subject to some constraints). In this setting, we give a bidirected network flowbased algorithm that, by taking advantage of high coverage, accurately estimates the copy counts of repeats in a genome. Our second algorithm combines these predicted copy counts with matepair data in order to assemble the reads into contigs.We run our algorithms on simulated read data fromEscherichia coli and predict copy counts with extremely high accuracy, while assembling long contigs.
Ab Initio Whole Genome Shotgun Assembly With Mated Short Reads
"... Abstract. Next Generation Sequencing (NGS) technologies are capable of reading millions of short DNA sequences both quickly and cheaply. While these technologies are already being used for resequencing individuals once a reference genome exists, it has not been shown if it is possible to use them fo ..."
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Abstract. Next Generation Sequencing (NGS) technologies are capable of reading millions of short DNA sequences both quickly and cheaply. While these technologies are already being used for resequencing individuals once a reference genome exists, it has not been shown if it is possible to use them for ab initio genome assembly. In this paper, we give a novel network flowbased algorithm that, by taking advantage of the high coverage provided by NGS, accurately estimates the copy counts of repeats in a genome. We also give a second algorithm that combines the predicted copycounts with matepair data in order to assemble the reads into contigs. We run our algorithms on simulated read data from E. Coli and predict copycounts with extremely high accuracy, while assembling long contigs. 1
Approximability of sparse integer programs
 In Proc. 17th ESA
, 2009
"... The main focus of this paper is a pair of new approximation algorithms for sparse integer programs. First, for covering integer programs {min cx: Ax ≥ b,0 ≤ x ≤ d} where A has at most k nonzeroes per row, we give a kapproximation algorithm. (We assume A, b, c, d are nonnegative.) For any k ≥ 2 and ..."
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The main focus of this paper is a pair of new approximation algorithms for sparse integer programs. First, for covering integer programs {min cx: Ax ≥ b,0 ≤ x ≤ d} where A has at most k nonzeroes per row, we give a kapproximation algorithm. (We assume A, b, c, d are nonnegative.) For any k ≥ 2 and ǫ> 0, if P = NP this ratio cannot be improved to k − 1 − ǫ, and under the unique games conjecture this ratio cannot be improved to k − ǫ. One key idea is to replace individual constraints by others that have better rounding properties but the same nonnegative integral solutions; another critical ingredient is knapsackcover inequalities. Second, for packing integer programs {max cx: Ax ≤ b,0 ≤ x ≤ d} where A has at most k nonzeroes per column, we give a 2 k k 2approximation algorithm. This is the first polynomialtime approximation algorithm for this problem with approximation ratio depending only on k, for any k> 1. Our approach starts from iterated LP relaxation, and then uses probabilistic and greedy methods to recover a feasible solution. Note added after publication: This version includes subsequent developments: a O(k 2) approximation for the latter problem using the iterated rounding framework, and several literature reference updates including a O(k)approximation for the same problem by Bansal et al.
The Two Variable Per Inequality Abstract Domain
 Higher Order and Symbolic Computation
"... Abstract. This article presents the Two Variable Per Inequality abstract domain (TVPI domain for short). This socalled weaklyrelational domain is able to express systems of linear inequalities where each inequality has at most two variables. The domain represents a sweetpoint in the performancec ..."
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Abstract. This article presents the Two Variable Per Inequality abstract domain (TVPI domain for short). This socalled weaklyrelational domain is able to express systems of linear inequalities where each inequality has at most two variables. The domain represents a sweetpoint in the performancecost tradeoff between the faster Octagon domain and the more expressive domain of general convex polyhedra. In particular, we detail techniques to closely approximate integral TVPI systems, thereby finessing the problem of excessively growing coefficients, yielding – to our knowledge – the only relational domain that combines linear relations with arbitrary coefficients and strongly polynomial performance.
Trajectory Tracking Control of a Timed Event Graph with Specifications Defined by a Ptime Event Graph: Online control and Offline preparation.
"... Abstract: The topic of this paper is the online trajectory tracking control on a sliding horizon of Timed Event Graphs with specifications defined by a Ptime Event Graph. Making the most of the specific structures of the systems, the CPU time of the online procedure is drastically reduced with tw ..."
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Abstract: The topic of this paper is the online trajectory tracking control on a sliding horizon of Timed Event Graphs with specifications defined by a Ptime Event Graph. Making the most of the specific structures of the systems, the CPU time of the online procedure is drastically reduced with two techniques: The use of specific algorithms of the graph theory instead of generic algorithms; an offline preparation which avoid the useless repetition of the same calculations. As a consequence, the approach can deal with long horizons and important systems and the application field of the trajectory tracking control is expanded. Keywords: Timed Event Graph, Ptime Petri Nets, Model predictive control, (max,+) algebra, large scale systems.
Strongly polynomial algorithm for generalized flow maximization
, 2013
"... A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every d ..."
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A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted. The full version is available on arXiv:1307.6809. The generalized flow model is a classical extension of network flows. Besides the capacity constraints, for every arc e there is a gain factor γe> 0, such that flow amount gets multiplied by γe while traversing the arc e. We study the flow maximization problem, where the objective is to send the maximum amount of flow to a sink node t. The model was already formulated by Kantorovich [17], as one of the first examples of linear programming; it has several applications in operations research [2, Chapter 15]. Gain factors can be used to model physical changes such as leakage or theft. Other common applications use the nodes to represent different types of entities, e.g. different currencies, and the gain factors correspond to the exchange rates. The existence of a strongly polynomial algorithm for linear programming is a major open question
Finding a Nonempty Algebraic Subset of an Edge Set in Linear Time
, 2005
"... A set of edges of a hypergraph H is an algebraic set if its characteristic vector can be expressed as a linear combination of rows of the (nodeedge) incidence matrix of H. Recently it was proven that deciding whether or not a given edgeset of H contains a nonempty algebraic set is an NPcomplete p ..."
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A set of edges of a hypergraph H is an algebraic set if its characteristic vector can be expressed as a linear combination of rows of the (nodeedge) incidence matrix of H. Recently it was proven that deciding whether or not a given edgeset of H contains a nonempty algebraic set is an NPcomplete problem. In this paper we give a linear time algorithm to decide if a given edgeset contains a nonempty algebraic set when the hypergraph is a graph.
Abstract ARTICLE IN PRESS
, 2007
"... www.elsevier.com/locate/tcs An analytical approach to the inference of summary data of additive type ..."
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www.elsevier.com/locate/tcs An analytical approach to the inference of summary data of additive type