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27
Finding Odd Cycle Transversals
, 2003
"... We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k. ..."
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Cited by 96 (2 self)
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We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k.
Robot Analysis
 Proc. of IEEE COMPSAC
, 1999
"... In this paper, we develop a probabilistic model to approach two realistic scenarios regarding the singular haplotype reconstruction problem the incompleteness and inconsistency occurred in the DNA sequencing process to generate the input haplotype fragments and the common practice used to generate ..."
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Cited by 67 (2 self)
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In this paper, we develop a probabilistic model to approach two realistic scenarios regarding the singular haplotype reconstruction problem the incompleteness and inconsistency occurred in the DNA sequencing process to generate the input haplotype fragments and the common practice used to generate synthetic data in experimental algorithm studies. We design three algorithms in the model that can reconstruct the two unknown haplotypes from the given matrix of haplotype fragments with provable high probability and in time linear in the size of the input matrix. We also present experimental results that conform with the theoretical efficient performance of those algorithms. The software of our algorithms is available for public access and for realtime online demonstration.
Y: Haplotype inference by maximum parsimony
 Bioinformatics
"... Motivation: Haplotypes have been attracting increasing attention because of their importance in analysis of many finescale moleculargenetics data. Since direct sequencing of haplotype via experimental methods is both timeconsuming and expensive, haplotype inference methods that infer haplotypes b ..."
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Cited by 64 (4 self)
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Motivation: Haplotypes have been attracting increasing attention because of their importance in analysis of many finescale moleculargenetics data. Since direct sequencing of haplotype via experimental methods is both timeconsuming and expensive, haplotype inference methods that infer haplotypes based on genotype samples become attractive alternatives. Results: (1) We design and implement an algorithm for an important computational model of haplotype inference that has been suggested before in several places. The model finds a set of minimum number of haplotypes that explains the genotype samples. (2) Strong supports of this computational model are given based on the computational results on both real data and simulation data. (3) We also did some comparative study to show the strength and weakness of this computational model using our program. Availability: The software HAPAR is free for noncommercial uses. Available upon request (lwang@cs.cityu.edu.hk). Contact:
A survey of computational methods for determining haplotypes
 Lecture Notes in Computer Science (2983): Computational Methods for SNPs and Haplotype Inference
, 2004
"... Abstract. It is widely anticipated that the study of variation in the human genome will provide a means of predicting risk of a variety of complex diseases. Single nucleotide polymorphisms (SNPs) are the most common form of genomic variation. Haplotypes have been suggested as one means for reducing ..."
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Cited by 38 (4 self)
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Abstract. It is widely anticipated that the study of variation in the human genome will provide a means of predicting risk of a variety of complex diseases. Single nucleotide polymorphisms (SNPs) are the most common form of genomic variation. Haplotypes have been suggested as one means for reducing the complexity of studying SNPs. In this paper we review some of the computational approaches that have been taking for determining haplotypes and suggest new approaches. 1
The Haplotyping Problem: An Overview of Computational Models and Solutions
 Journal of Computer Science and Technology
, 2003
"... The investigation of genetic di#erences among humans has given evidence that mutations in DNA sequences are responsible for some genetic diseases. The most common mutation is the one that involves only a single nucleotide of the DNA sequence, which is called a single nucleotide polymorphism (SNP) ..."
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Cited by 34 (5 self)
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The investigation of genetic di#erences among humans has given evidence that mutations in DNA sequences are responsible for some genetic diseases. The most common mutation is the one that involves only a single nucleotide of the DNA sequence, which is called a single nucleotide polymorphism (SNP). As a consequence, computing a complete map of all SNPs occurring in the human populations is one of the primary goals of recent studies in human genomics. The construction of such a map requires to determine the DNA sequences that from all chromosomes. In diploid organisms like humans, each chromosome consists of two sequences called haplotypes.
An MCMC algorithm for haplotype assembly from whole genome sequence data
 Genome Res
, 2008
"... sequence data ..."
Algorithm Engineering for Optimal Graph Bipartization
, 2009
"... We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental ..."
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Cited by 21 (4 self)
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We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental results. The worstcase time complexity is improved. Based on new structural insights, we give a simplified correctness proof. This also allows us to establish a heuristic improvement that in particular speeds up the search on dense graphs. Our best algorithm can solve all instances from a testbed from computational biology within minutes, whereas established methods are only able to solve about half of the instances within reasonable time.
Combinatorial problems arising in SNP and Haplotype Analysis
 Discrete Mathematics and Theoretical Computer Science. Proceedings of DMTCS 2003
, 2003
"... Abstract. It is widely anticipated that the study of variation in the human genome will provide a means of predicting riskof a variety of complex diseases. This paper presents a number of algorithmic and combinatorial problems that arise when studying a very common form of genomic variation, single ..."
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Cited by 14 (2 self)
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Abstract. It is widely anticipated that the study of variation in the human genome will provide a means of predicting riskof a variety of complex diseases. This paper presents a number of algorithmic and combinatorial problems that arise when studying a very common form of genomic variation, single nucleotide polymorphisms (SNPs). We review recent results and present challenging open problems. 1
Fosmidbased whole genome haplotyping of a HapMap trio child: evaluation of Single Individual Haplotyping techniques
, 2011
"... Determining the underlying haplotypes of individual human genomes is an essential, but currently difficult, step toward a complete understanding of genome function. Fosmid poolbased nextgeneration sequencing allows genomewide generation of 40kb haploid DNA segments, which can be phased into conti ..."
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Cited by 13 (0 self)
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Determining the underlying haplotypes of individual human genomes is an essential, but currently difficult, step toward a complete understanding of genome function. Fosmid poolbased nextgeneration sequencing allows genomewide generation of 40kb haploid DNA segments, which can be phased into contiguous molecular haplotypes computationally by Single Individual Haplotyping (SIH). Many SIH algorithms have been proposed, but the accuracy of such methods has been difficult to assess due to the lack of real benchmark data. To address this problem, we generated whole genome fosmid sequence data from a HapMap trio child, NA12878, for which reliable haplotypes have already been produced. We assembled haplotypes using eight algorithms for SIH and carried out direct comparisons of their accuracy, completeness and efficiency. Our comparisons indicate that fosmidbased haplotyping can deliver highly accurate results even at low coverage and that our SIH algorithm, ReFHap, is able to efficiently produce highquality haplotypes. We expanded the haplotypes for NA12878 by combining the current haplotypes with our fosmidbased haplotypes, producing neartocomplete new goldstandard haplotypes containing almost 98 % of heterozygous SNPs. This improvement includes notable fractions of diseaserelated and GWA SNPs. Integrated with other molecular biological data sets, this phase information will advance the emerging field of diploid genomics.
Linear Time Probabilistic Algorithms for the Singular Haplotype Reconstruction Problem from SNP Fragments
"... In this paper, we develop a probabilistic model to approach two scenarios in reality about the singular haplotype reconstruction problem the incompleteness and inconsistency occurred in the DNA sequencing process to generate the input haplotype fragments and the common practice used to generate syn ..."
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Cited by 12 (3 self)
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In this paper, we develop a probabilistic model to approach two scenarios in reality about the singular haplotype reconstruction problem the incompleteness and inconsistency occurred in the DNA sequencing process to generate the input haplotype fragments and the common practice used to generate synthetic data in experimental algorithm studies. We design three algorithms in the model that can reconstruct the two unknown haplotypes from the given matrix of haplotype fragments with provable high probability and in time linear in the size of the input matrix. We also present experimental results that conform with the theoretical efficient performance of those algorithms. The software of our algorithms is available for public access and for realtime online demonstration. 1.