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Haplotyping as Perfect Phylogeny: Conceptual Framework and Efficient Solutions (Extended Abstract)
, 2002
"... The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strat ..."
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Cited by 109 (10 self)
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The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strategy is presently being finalized by an NIH workinggroup. The biological key to that strategy is the surprising fact that genomic DNA can be partitioned into long blocks where genetic recombination has been rare, leading to strikingly fewer distinct haplotypes in the population than previously expected [12, 6, 21, 7]. In this paper
Haplotype reconstruction from genotype data using imperfect phylogeny
 Bioinformatics
, 2004
"... Critical to the understanding of the genetic basis for complex diseases is the modeling of human variation. Most of this variation can be characterized by single nucleotide polymorphisms (SNPs) which are mutations at a single nucleotide position. To characterize the genetic variation between differe ..."
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Cited by 70 (5 self)
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Critical to the understanding of the genetic basis for complex diseases is the modeling of human variation. Most of this variation can be characterized by single nucleotide polymorphisms (SNPs) which are mutations at a single nucleotide position. To characterize the genetic variation between different people, we must determine an individual’s haplotype or which nucleotide base occurs at each position of these common SNPs for each chromosome. In this paper, we present results for a highly accurate method for haplotype resolution from genotype data. Our method leverages a new insight into the underlying structure of haplotypes which shows that SNPs are organized in highly correlated “blocks”. In a few recent studies (see Daly et al. (2001); Patil et al. (2001)), considerable parts of the human genome were partitioned into blocks, such that the majority of the sequenced genotypes have one of about four common haplotypes in each block. Our method partitions the SNPs into blocks and for each block, we predict the common haplotypes and each individual’s haplotype. We evaluate our method over biological data. Our method predicts the common haplotypes perfectly and has a very low error rate (less than ¢ ¡ over the data from Daly et al. (2001).) when taking into account the predictions for the uncommon haplotypes. Our method is extremely efficient compared to previous methods, such as PHASE and HAPLOTYPER. Its efficiency allows us to find the block partition of the haplotypes, to cope with missing data and to work with large data sets. Availability: The algorithm is available via webserver at
Efficient reconstruction of haplotype structure via perfect phylogeny
 Journal of Bioinformatics and Computational Biology
, 2003
"... Each person’s genome contains two copies of each chromosome, one inherited from the father and the other from the mother. A person’s genotype specifies the pair of bases at each site, but does not specify which base occurs on which chromosome. The sequence of each chromosome separately is called a h ..."
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Cited by 68 (10 self)
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Each person’s genome contains two copies of each chromosome, one inherited from the father and the other from the mother. A person’s genotype specifies the pair of bases at each site, but does not specify which base occurs on which chromosome. The sequence of each chromosome separately is called a haplotype. The determination of the haplotypes within a population is essential for understanding genetic variation and the inheritance of complex diseases. The haplotype mapping project, a successor to the human genome project, seeks to determine the common haplotypes in the human population. Since experimental determination of a person’s genotype is less expensive than determining its component haplotypes, algorithms are required for computing haplotypes from genotypes. Two observations aid in this process: first, the human genome contains short blocks within which only a few different haplotypes occur; second, as suggested by Gusfield, it is reasonable to assume that the haplotypes observed within a block have evolved according to a perfect phylogeny, in which at most one mutation event has occurred at any site, and no recombination occurred at the given region. We present a simple and efficient polynomialtime algorithm for inferring haplotypes from the genotypes of a set of individuals assuming a perfect phylogeny. Using a reduction to 2SAT we extend this algorithm to handle constraints that apply when we have genotypes from both parents and child. We also present a hardness result for the problem of removing the minimum number of individuals from a population to ensure that the genotypes of the remaining individuals are consistent with a perfect phylogeny. Our algorithms have been tested on real data and give biologically meaningful results. Our webserver
Modelbased inference of haplotype block variation
 Proceedings of the Seventh Annual International Conference on Computational Molecular Biology (RECOMB 2003
, 2003
"... The uneven recombination structure of human DNA has been highlighted by several recent studies. Knowledge of the haplotype blocks generated by this phenomenon can be applied to dramatically increase the statistical power of genetic mapping. Several criteria have already been proposed for identifying ..."
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Cited by 49 (6 self)
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The uneven recombination structure of human DNA has been highlighted by several recent studies. Knowledge of the haplotype blocks generated by this phenomenon can be applied to dramatically increase the statistical power of genetic mapping. Several criteria have already been proposed for identifying these blocks, all of which require haplotypes as input. We propose a comprehensive statistical model of haplotype block variation and show how the parameters of this model can be learned from haplotypes and/or unphased genotype data. Using realworld SNP data, we demonstrate that our approach can be used to resolve genotypes into their constituent haplotypes with greater accuracy than previously known methods.
Large scale reconstruction of haplotypes from genotype data
 In Proc. RECOMB’03
, 2003
"... Critical to the understanding of the genetic basis for complex diseases is the modeling of human variation. Most of this variation can be characterized by single nucleotide polymorphisms (SNPs) which are mutations at a single nucleotide position. To characterize an individual’s variation, we must de ..."
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Cited by 45 (2 self)
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Critical to the understanding of the genetic basis for complex diseases is the modeling of human variation. Most of this variation can be characterized by single nucleotide polymorphisms (SNPs) which are mutations at a single nucleotide position. To characterize an individual’s variation, we must determine an individual’s haplotype or which nucleotide base occurs at each position of these common SNPs for each chromosome. In this paper, we present results for a highly accurate method for haplotype resolution from genotype data. Our method leverages a new insight into the underlying structure of haplotypes which shows that SNPs are organized in highly correlated “blocks”. The majority of individuals have one of about four common haplotypes in each block. Our method partitions the SNPs into blocks and for each block, we predict the common haplotypes and each individual’s haplotype. We evaluate our method over biological data. Our method predicts the common haplotypes perfectly and has a very low error rate (0.47%) when taking into account the predictions for the uncommon haplotypes. Our method is extremely efficient compared to previous methods, (a matter of seconds where previous methods needed hours). Its efficiency allows us to find the block partition of the haplotypes, to cope with missing data and to work with large data sets such as genotypes for thousands of SNPs for hundreds of individuals. The algorithm is available via webserver
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 44 (3 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 33 (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
Integer programming approaches to haplotype inference by pure parsimony
 IEEE/ACM Transactions on Computational Biology and Bioinformatics
, 2006
"... Abstract—In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield’s IP can be of exponential size in the worst case ..."
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Cited by 32 (2 self)
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Abstract—In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield’s IP can be of exponential size in the worst case. Several authors [2], [3] have presented polynomialsized IPs for the problem. In this paper, we further the work on IP approaches to HIPP. We extend the existing polynomialsized IPs by introducing several classes of valid cuts for the IP. We also present a new polynomialsized IP formulation that is a hybrid between two existing IP formulations and inherits many of the strengths of both. Many problems that are too complex for the exponentialsized formulations can still be solved in our new formulation in a reasonable amount of time. We provide a detailed empirical comparison of these IP formulations on both simulated and real genotype sequences. Our formulation can also be extended in a variety of ways to allow errors in the input or model the structure of the population under consideration. Index Terms—Computations on discrete structures, integer programming, biology and genetics, haplotype inference. 1
An approximation algorithm for haplotype inference by maximum parsimony
 Journal of Computational Biology
, 2005
"... This paper studies haplotype inference by maximum parsimony using population data. We define the optimal haplotype inference (OHI) problem as given a set of genotypes and a set of related haplotypes, find a minimum subset of haplotypes that can resolve all the genotypes. We prove that OHI is NPhard ..."
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Cited by 28 (1 self)
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This paper studies haplotype inference by maximum parsimony using population data. We define the optimal haplotype inference (OHI) problem as given a set of genotypes and a set of related haplotypes, find a minimum subset of haplotypes that can resolve all the genotypes. We prove that OHI is NPhard and can be formulated as an integer quadratic programming (IQP) problem. To solve the IQP problem, we propose an iterative semidefinite programming based approximation algorithm, (called SDPHapInfer). We show that this algorithm finds a solution within a factor of O(log n) of the optimal solution, where n is the number of genotypes. This algorithm has been implemented and tested on a variety of simulated and biological data. In comparison with three other methods: (1) HAPAR, which was implemented based on the branching and bound algorithm, (2) HAPLOTYPER, which was implemented based on the ExpectationMaximization algorithm, and (3) PHASE, which combined the Gibbs sampling algorithm with an approximate coalescent prior, the experimental results indicate that SDPHapInfer and HAPLOTYPER have similar error rates. In addition, the results generated by PHASE have lower error rates on some data but higher error rates on others. The error rates of HAPAR are higher than the others on biological data. In
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 26 (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.