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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 111 (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
A lineartime algorithm for the perfect phylogeny haplotyping (PPH) problem
 In International Conference on Research in Computational Molecular Biology (RECOMB
, 2005
"... Since the introduction of the Perfect Phylogeny Haplotyping (PPH) Problem in RECOMB 2002 (Gusfield, 2002), the problem of finding a lineartime (deterministic, worstcase) solution for it has remained open, despite broad interest in the PPH problem and a series of papers on various aspects of it. In ..."
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Cited by 30 (8 self)
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Since the introduction of the Perfect Phylogeny Haplotyping (PPH) Problem in RECOMB 2002 (Gusfield, 2002), the problem of finding a lineartime (deterministic, worstcase) solution for it has remained open, despite broad interest in the PPH problem and a series of papers on various aspects of it. In this paper, we solve the open problem, giving a practical, deterministic lineartime algorithm based on a simple data structure and simple operations on it. The method is straightforward to program and has been fully implemented. Simulations show that it is much faster in practice than prior nonlinear methods. The value of a lineartime solution to the PPH problem is partly conceptual and partly for use in the inner loop of algorithms for more complex problems, where the PPH problem must be solved repeatedly. Key words: Perfect Phylogeny Haplotyping (PPH) Problem, Haplotype Inference Problem, lineartime algorithm, shadow tree. 1.
An Overview of Combinatorial Methods for Haplotype Inference
 Lecture Notes in Computer Science (2983): Computational Methods for SNPs and Haplotype Inference
, 2004
"... A current highpriority phase of human genomics involves the development of a full Haplotype Map of the human genome [23]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A key, perhaps bottleneck, problem is t ..."
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Cited by 23 (2 self)
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A current highpriority phase of human genomics involves the development of a full Haplotype Map of the human genome [23]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A key, perhaps bottleneck, problem is to computationally infer haplotype pairs from genotype data. This paper follows the talk given at the DIMACS Conference on SNPs and Haplotypes held in November of 2002. It reviews several combinatorial approaches to the haplotype inference problem that we have investigated over the last several years. In addition, it updates some of the work presented earlier, and discusses the current state of our work. 1 Introduction to SNP’s, Genotypes and Haplotypes In diploid organisms (such as humans) there are two (not completely identical) “copies ” of each chromosome, and hence of each region of interest.
Algorithms for imperfect phylogeny haplotyping (ipph) with a single homoplasy or recombination event
 Proceedings of Workshop on Algorithms in Bioinformatics 2005, Lecture Notes in Computer Science 3692
, 2005
"... Abstract. The haplotype inference (HI) problem is the problem of inferring 2n haplotype pairs from n observed genotype vectors. This is a key problem that arises in studying genetic variation in populations, for example in the ongoing HapMap project [5]. In order to have a hope of finding the haplot ..."
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Cited by 15 (2 self)
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Abstract. The haplotype inference (HI) problem is the problem of inferring 2n haplotype pairs from n observed genotype vectors. This is a key problem that arises in studying genetic variation in populations, for example in the ongoing HapMap project [5]. In order to have a hope of finding the haplotypes that actually generated the observed genotypes, we must use some (implicit or explicit) genetic model of the evolution of the underlying haplotypes. The Perfect Phylogeny Haplotyping (PPH) model was introduced in 2002 [9] to reflect the “neutral coalescent ” or “perfect phylogeny ” model of haplotype evolution. The PPH problem (which can be solved in polynomial time) is to determine whether there is an HI solution where the inferred haplotypes can be derived on a perfect phylogeny (tree). Since the introduction of the PPH model, several extensions and modifications of the PPH model have been examined. The most important modification, to model biological reality better, is to allow a limited number of biological events that violate the perfect phylogeny model. This was accomplished implicitly in [7,12] with the inclusion of several heuristics into an algorithm for the PPH problem [8]. Those heuristics are invoked when the genotype data cannot be explained with haplotypes that fit the perfect phylogeny model. In this paper, we address the issue explicitly, by allowing one recombination or homoplasy event in the model of haplotype evolution. We formalize the problems and provide a polynomial time solution for one problem, using an additional, empiricallysupported assumption. We present a related framework for the second problem which gives a practical algorithm. We believe the second problem can be solved in polynomial time. 1
An efficientlycomputed lower bound on the number of recombinations in phylogenetic networks: Theory and empirical study
 Discrete Applied Math, special issue on Computational Biology
, 2004
"... Phylogenetic networks are models of sequence evolution that go beyond trees, allowing biological operations that are not treelike. One of the most important biological operations is recombination between two sequences. An established problem ..."
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Cited by 8 (4 self)
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Phylogenetic networks are models of sequence evolution that go beyond trees, allowing biological operations that are not treelike. One of the most important biological operations is recombination between two sequences. An established problem
Computer Algebra in the Life Sciences
 SIGSAM Bull
"... This note (1) provides references to recent work that applies computer algebra (CA) to the life sciences, (2) cites literature that explains the biological background of each application, (3) states the mathematical methods that are used, (4) mentions the benefits of CA, and (5) suggests some topi ..."
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Cited by 3 (0 self)
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This note (1) provides references to recent work that applies computer algebra (CA) to the life sciences, (2) cites literature that explains the biological background of each application, (3) states the mathematical methods that are used, (4) mentions the benefits of CA, and (5) suggests some topics for future work.
Populations
"... A current high priority research goal is to understand how genetic variations influence complex genetic diseases (or more generally traits). Recombination is an important biological and genetic process that plays a major role in the logic behind association mapping, a currently intensely studied met ..."
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Cited by 1 (0 self)
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A current high priority research goal is to understand how genetic variations influence complex genetic diseases (or more generally traits). Recombination is an important biological and genetic process that plays a major role in the logic behind association mapping, a currently intensely studied method widely hoped to efficiently find genes (alleles) associated with complex diseases. Recently, populationscale genetic variation data has become increasingly available. In this dissertation, I will present algorithmic and computational results on inferring historical recombination and constructing genealogical networks with recombination. I will demonstrate applications of these results to two biologically important problems: detecting recombination hotspots and association mapping of complex diseases. A central computational problem in this dissertation is the recombination minimization problem. I will first describe methods that compute lower bounds on the minimum number of recombinations needed to derive a set of SNP sequences and its application in detecting recombination hotspots. I will also present methods for detecting recombination hotspots and association mapping using genealogical networks. For both biological problems, I will demonstrate the effectiveness of these methods with experimental results on simulated or real data.
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"... Abstract. The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of genetic mutations. In order to find the haplotypes which are as close as poss ..."
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Abstract. The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of genetic mutations. In order to find the haplotypes which are as close as possible to the real set of haplotypes that comprise the genotypes, two models have been suggested which are by now wellstudied: The perfect phylogeny model and the pure parsimony model. All known algorithms up till now for haplotype inference may find haplotypes that are not necessarily plausible, i.e. very rare haplotypes or haplotypes that were never observed in the population. In order to overcome this disadvantage we study in this paper a new constrained version of HIP under the above mentioned models. In this new version, a pool of plausible haplotypes ˜ H is given together with the set of genotypes G, and the goal is to find a subset H ⊆ ˜ H that resolves G. For constrained perfect phylogeny haplotyping (CPPH), we provide initial insights and polynomialtime algorithms for some restricted cases of the problem. For constrained parsimony haplotyping (CPH), we show that the problem is fixed parameter tractable when parameterized by the size of the solution set of haplotypes.