Linear-Time Haplotype Inference on Pedigrees Without Recombinations

Chan, Mei‐Yee; Chan, Wai-Sum; Chin, Francis Y. L.; Fung, Stanley P. Y.; Kao, Ming-Yang

doi:10.1007/11851561_6

Cited by 22 publications

(26 citation statements)

References 6 publications

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“…Several attempts have been made by Chin and Zhang 28 and Li et al, 29 but the authors failed to prove the correctness of their algorithms in all cases, especially when the input pedigree has mating loops. Chan et al 30 proposed a linear-time algorithm, but the algorithm only works for pedigrees without mating loops (i.e. the tree pedigrees).…”

Section: Algorithms For Zrhc-formentioning

confidence: 99%

A Survey on Haplotyping Algorithms for Tightly Linked Markers

Jiang

2008

J. Bioinform. Comput. Biol.

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Two grand challenges in the postgenomic era are to develop a detailed understanding of heritable variation in the human genome, and to develop robust strategies for identifying the genetic contribution to diseases and drug responses. Haplotypes of single nucleotide polymorphisms (SNPs) have been suggested as an effective representation of human variation, and various haplotype-based association mapping methods for complex traits have been proposed in the literature. However, humans are diploid and, in practice, genotype data instead of haplotype data are collected directly. Therefore, efficient and accurate computational methods for haplotype reconstruction are needed and have recently been investigated intensively, especially for tightly linked markers such as SNPs. This paper reviews statistical and combinatorial haplotyping algorithms using pedigree data, unrelated individuals, or pooled samples.

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Section: Algorithms For Zrhc-formentioning

confidence: 99%

A Survey on Haplotyping Algorithms for Tightly Linked Markers

Jiang

2008

J. Bioinform. Comput. Biol.

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“…We have . By plugging in the solution of h variables in Equation 2, we will finally get a general solution for the ZRHC problem, (3) If is not pre-determined, we have one more degree of freedom in Equation 3.…”

Section: Offset[rep[j]] ← Offset[j] + Offset[i] + C Rep[rep[j]] ← Repmentioning

confidence: 99%

“…Here, a particular solution means a specific assignment for each variable which satisfies the constraints, while a general solution is a description of all solutions in a general form where some variables are designated as free (meaning that they are allowed to take any value), and the remaining variables are represented by a linear combination of these free variables. For tree pedigrees, Chan et al 3 further reduce the complexity of finding a particular solution to a linear time O(mn) by manipulating the constraints on a graph structure. Liu and Jiang12 also propose an algorithm to produce a particular solution in O(mn) and a general solution in O(mn 2 ) by further exploring features of their h variable system on a tree pedigree.…”

Section: Introductionmentioning

confidence: 99%

Efficient Haplotype Inference From Pedigrees With Missing Data Using Linear Systems With Disjoint-Set Data Structures

2008

Computational Systems Bioinformatics

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We study the haplotype inference problem from pedigree data under the zero recombination assumption, which is well supported by real data for tightly linked markers (i.e., single nucleotide polymorphisms (SNPs)) over a relatively large chromosome segment. We solve the problem in a rigorous mathematical manner by formulating genotype constraints as a linear system of inheritance variables. We then utilize disjoint-set structures to encode connectivity information among individuals, to detect constraints from genotypes, and to check consistency of constraints. On a tree pedigree without missing data, our algorithm can output a general solution as well as the number of total specific solutions in a nearly linear time O(mn · α(n)), where m is the number of loci, n is the number of individuals and α is the inverse Ackermann function4, which is a further improvement over existing ones3 , 8 , 12 , 15. We also extend the idea to looped pedigrees and pedigrees with missing data by considering existing (partial) constraints on inheritance variables. The algorithm has been implemented in C++ and will be incorporated into our PedPhase package8. Experimental results show that it can correctly identify all 0-recombinant solutions with great efficiency. Comparisons with other two popular algorithms show that the proposed algorithm achieves 10 to 10 5 -fold improvements over a variety of parameter settings. The experimental study also provides empirical evidences on the complexity bounds suggested by theoretical analysis.

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“…It is unclear how the algorithm can be extended to produce general solutions efficiently. Moreover, the algorithm has four different stages and needs to maintain various consistency conditions (called SNPconsistency, Mendelian consistency, and endgame-consistency) and avoid some inconsistency conditions (such as the family problem) at these stages (see [4] for the details of the (in)consistency conditions). As a result, the analysis of the algorithm (concerning both correctness and complexity) is quite involved.…”

Section: Introductionmentioning

confidence: 99%

Linear-Time Reconstruction of Zero-Recombinant Mendelian Inheritance on Pedigrees without Mating Loops

Liu

Jiang

2007

Genome Informatics 2007

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With the launch of the international HapMap project, the haplotype inference problem has attracted a great deal of attention in the computational biology community recently. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree without mating loops, assuming that the hereditary process was free of mutations (i.e. the Mendelian law of inheritance) and recombinants. We model the haplotype inference problem as a system of linear equations as in [10] and present an (optimal) linear-time (i.e. O(mn) time) algorithm to generate a particular solution * to the haplotype inference problem, where m is the number of loci (or markers) in a genotype and n is the number of individuals in the pedigree. Moreover, the algorithm also provides a general solution † in O(mn 2 ) time, which is optimal because the size of a general solution could be as large as Θ(mn 2 ). The key ingredients of our construction are (i) a fast consistency checking procedure for the system of linear equations introduced in [10] based on a careful investigation of the relationship between the equations (ii) a novel linear-time method for solving linear equations without invoking the Gaussian elimination method. Although such a fast method for solving equations is not known for general systems of linear equations, we take advantage of the underlying loop-free pedigree graph and some special properties of the linear equations.

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Linear-Time Haplotype Inference on Pedigrees Without Recombinations

Cited by 22 publications

References 6 publications

A Survey on Haplotyping Algorithms for Tightly Linked Markers

A Survey on Haplotyping Algorithms for Tightly Linked Markers

Efficient Haplotype Inference From Pedigrees With Missing Data Using Linear Systems With Disjoint-Set Data Structures

Linear-Time Reconstruction of Zero-Recombinant Mendelian Inheritance on Pedigrees without Mating Loops

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