A Survey on Haplotyping Algorithms for Tightly Linked Markers

Li, Jing; Jiang, Tao

doi:10.1142/s0219720008003369

Cited by 17 publications

(13 citation statements)

References 49 publications

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“…In this paper, we assume all alleles are bi-allelic (0 or 1). The genotypes of individual j is denoted as a ternary vector g j and its kth entry g j [k] represents the genotype at locus k of individual j: For individual j, we define p j ∈ GF (2) m as the paternal haplotype of individual j. Each entry…”

Section: The Linear Systemmentioning

confidence: 99%

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Inferring Haplotypes From Genotypes on a Pedigree With Mutations, Genotyping Errors and Missing Alleles

Wang

Jiang

2011

J. Bioinform. Comput. Biol.

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Inferring the haplotypes of the members of a pedigree from their genotypes has been extensively studied. However, most studies do not consider genotyping errors and de novo mutations. In this paper, we study how to infer haplotypes from genotype data which may contain genotyping errors, de novo mutations and missing alleles. We assume that there are no recombinants in the genotype data, which is usually true for tightly linked markers. We introduce a combinatorial optimization problem, called haplotype configuration with mutations and errors (HCME), which calls for haplotype configurations consistent with the given genotypes that incur no recombinants and require the minimum number of mutations and errors. HCME is NP-hard. To solve the problem, we propose a heuristic algorithm, the core of which is an integer linear program (ILP) using the system of linear equations over Galois field GF(2). Our algorithm can detect and locate genotyping errors that cannot be detected by simply checking the Mendelian law of inheritance. The algorithm also offers error correction in genotypes/haplotypes rather than just detecting inconsistencies and deleting the involved loci. Our experimental results show that the algorithm can infer haplotypes with a very high accuracy, and recover 65%-94% of genotyping errors depending on the pedigree topology.

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Section: The Linear Systemmentioning

confidence: 99%

“…To represent the maternal haplotype of individual j, we define w j ∈ GF (2) m to indicate if each locus of individual j is heterozygous. That is,…”

Section: The Linear Systemmentioning

confidence: 99%

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Inferring Haplotypes From Genotypes on a Pedigree With Mutations, Genotyping Errors and Missing Alleles

Wang

Jiang

2011

J. Bioinform. Comput. Biol.

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“…The first problem is that the genomic data generated by many sequencing experiments does not produce the haplotypes of an individual, but rather a mixture of both haplotypes, the so-called genotype. It is a challenging problem by itself to compute the haplotypes from the genotype, but some successful algorithms have been presented in the literature, for an overview see, for example, [2,11,3].…”

Section: Application To a Haplotype Classification Problemmentioning

confidence: 99%

The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification

Böckenhauer

Forišek

Oravec

et al. 2010

RAIRO-Theor. Inf. Appl.

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Abstract. Analyzing genomic data for finding those gene variations which are responsible for hereditary diseases is one of the great challenges in modern bioinformatics. In many living beings (including the human), every gene is present in two copies, inherited from the two parents, the so-called haplotypes. In this paper, we propose a simple combinatorial model for classifying the set of haplotypes in a population according to their responsibility for a certain genetic disease. This model is based on the minimum-ones 2SAT problem with uniform clauses. The minimum-ones 2SAT problem asks for a satisfying assignment to a satisfiable formula in 2CNF which sets a minimum number of variables to true. This problem is well-known to be N P-hard, even in the case where all clauses are uniform, i. e., do not contain a positive and a negative literal. We analyze the approximability and present the first non-trivial exact algorithm for the uniform minimum-ones 2SAT problem with a running time of O(1.25993 n ) on a 2SAT formula with n variables.

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“…Since genotype data instead of haplotype data are routinely collected in practice, especially in large-scale sequencing projects, due to cost considerations, efficient and accurate computational methods for the inference of haplotypes from genotypes over a set of marker loci, which is also commonly referred to as phasing, have been extensively studied in the literature. See [11] for a recent survey on these methods as well as the basic concepts involved in haplotype inference.…”

Section: Introductionmentioning

confidence: 99%

Efficient Inference of Haplotypes from Genotypes on a Pedigree with Mutations and Missing Alleles (Extented Abstract)

Wang

Jiang

2009

Combinatorial Pattern Matching

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Abstract. Driven by the international HapMap project, the haplotype inference problem has become an important topic in the computational biology community. In this paper, we study how to efficiently infer haplotypes from genotypes of related individuals as given by a pedigree. Our assumption is that the input pedigree data may contain de novo mutations and missing alleles but is free of genotyping errors and recombinants, which is usually true for tightly linked markers. We formulate the problem as a combinatorial optimization problem, called the minimum mutation haplotype configuration (MMHC) problem, where we seek haplotypes consistent with the given genotypes that incur no recombinants and require the minimum number of mutations. This extends the well studied zero-recombinant haplotype configuration (ZRHC) problem. Although ZRHC is polynomial-time solvable, MMHC is NP-hard. We construct an integer linear program (ILP) for MMHC using the system of linear equations over the field F (2) that has been developed recently to solve ZRHC. Since the number of constraints in the ILP is large (exponentially large in the general case), we present an incremental approach for solving the ILP where we gradually add the constraints to a standard ILP solver until a feasible haplotype configuration is found. Our preliminary experiments on simulated data demonstrate that the method is very efficient on large pedigrees and can infer haplotypes very accurately as well as recover most of the mutations and missing alleles correctly.

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A Survey on Haplotyping Algorithms for Tightly Linked Markers

Cited by 17 publications

References 49 publications

Inferring Haplotypes From Genotypes on a Pedigree With Mutations, Genotyping Errors and Missing Alleles

Inferring Haplotypes From Genotypes on a Pedigree With Mutations, Genotyping Errors and Missing Alleles

The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification

Efficient Inference of Haplotypes from Genotypes on a Pedigree with Mutations and Missing Alleles (Extented Abstract)

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