A Near-Linear Time Algorithm for Haplotype Determination on General Pedigrees

Doan, Duong D.; Evans, Patricia; Horton, J. D.

doi:10.1089/cmb.2009.0133

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…Various haplotyping algorithms exist for non-recombinant pedigree data [1,2], especially a linear algorithm for tree pedigrees [1] and a near-linear algorithm for general pedigrees [2]. Haplotype inference is complicated by recombination events and the complex structures of the data.…”

Section: Introductionmentioning

confidence: 99%

“…In the absence of recombination events, haplotypes of members in a pedigree follow the Mendelian law of inheritance, where the two haplotypes of a child are transferred from its parents, one haplotype from its father and the other from its mother. Various haplotyping algorithms exist for non-recombinant pedigree data [ 1 , 2 ], especially a linear algorithm for tree pedigrees [ 1 ] and a near-linear algorithm for general pedigrees [ 2 ]. Haplotype inference is complicated by recombination events and the complex structures of the data.…”

Section: Introductionmentioning

confidence: 99%

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An FPT haplotyping algorithm on pedigrees with a small number of sites

Doan

Evans

2011

Algorithms Mol Biol

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BackgroundGenetic disease studies investigate relationships between changes in chromosomes and genetic diseases. Single haplotypes provide useful information for these studies but extracting single haplotypes directly by biochemical methods is expensive. A computational method to infer haplotypes from genotype data is therefore important. We investigate the problem of computing the minimum number of recombination events for general pedigrees with a small number of sites for all members.ResultsWe show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem with additional parity constraints. We solve this problem with an exact algorithm that runs in time, where n is the number of members, m is the number of sites, and k is the number of recombination events.ConclusionsThis algorithm infers haplotypes for a small number of sites, which can be useful for genetic disease studies to track down how changes in haplotypes such as recombinations relate to genetic disease.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An FPT haplotyping algorithm on pedigrees with a small number of sites

Doan

Evans

2011

Algorithms Mol Biol

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“…Xiao et al improved the method to take O ( mn 2 + n 3 log 2 n log log n ) time by removing redundant equations from the linear system [16]. Doan et al proposed an O ( mnα ( m )) time algorithm by exploring constraints among marker loci rather than family members, where α (·) is the inverse of the Ackermann function [14]. For tree pedigrees, the execution time of the algorithm proposed by Xiao can be reduced from O ( mn 2 + n 3 log 2 n log log n ) to O ( mn + n 3 ) [16].…”

Section: Introductionmentioning

confidence: 99%

A linear-time algorithm for reconstructing zero-recombinant haplotype configuration on a pedigree

et al. 2012

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BackgroundWhen studying genetic diseases in which genetic variations are passed on to offspring, the ability to distinguish between paternal and maternal alleles is essential. Determining haplotypes from genotype data is called haplotype inference. Most existing computational algorithms for haplotype inference have been designed to use genotype data collected from individuals in the form of a pedigree. A haplotype is regarded as a hereditary unit and therefore input pedigrees are preferred that are free of mutational events and have a minimum number of genetic recombinational events. These ideas motivated the zero-recombinant haplotype configuration (ZRHC) problem, which strictly follows the Mendelian law of inheritance, namely that one haplotype of each child is inherited from the father and the other haplotype is inherited from the mother, both without any mutation. So far no linear-time algorithm for ZRHC has been proposed for general pedigrees, even though the number of mating loops in a human pedigree is usually very small and can be regarded as constant.ResultsGiven a pedigree with n individuals, m marker loci, and k mating loops, we proposed an algorithm that can provide a general solution to the zero-recombinant haplotype configuration problem in O(kmn + k2m) time. In addition, this algorithm can be modified to detect inconsistencies within the genotype data without loss of efficiency. The proposed algorithm was subject to 12000 experiments to verify its performance using different (n, m) combinations. The value of k was uniformly distributed between zero and six throughout all experiments. The experimental results show a great linearity in terms of execution time in relation to input size when both n and m are larger than 100. For those experiments where n or m are less than 100, the proposed algorithm runs very fast, in thousandth to hundredth of a second, on a personal desktop computer.ConclusionsWe have developed the first deterministic linear-time algorithm for the zero-recombinant haplotype configuration problem. Our experimental results demonstrated the linearity of its execution time in relation to the input size. The proposed algorithm can be modified to detect inconsistency within the genotype data without loss of efficiency and is expected to be able to handle recombinant and missing data with further extension.

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“…Various haplotyping algorithms exist for non-recombinant pedigree data [2-5], especially a linear time algorithm for non-recombinant tree pedigrees [2] and a near-linear time algorithm for non-recombinant general pedigrees [3]. Haplotype inference is complicated by recombination events and the complex structures of the data themselves.…”

Section: Introductionmentioning

confidence: 99%

“…In the absence of recombination events, haplotypes of members in a pedigree follow the Mendelian law of inheritance, where the two haplotypes of a child are transferred from its parents, one haplotype from its father and the other from its mother. Various haplotyping algorithms exist for non-recombinant pedigree data [ 2 - 5 ], especially a linear time algorithm for non-recombinant tree pedigrees [ 2 ] and a near-linear time algorithm for non-recombinant general pedigrees [ 3 ]. Haplotype inference is complicated by recombination events and the complex structures of the data themselves.…”

Section: Introductionmentioning

confidence: 99%

Haplotype inference in general pedigrees with two sites

Doan

Evans

2011

BMC Proc

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BackgroundGenetic disease studies investigate relationships between changes in chromosomes and genetic diseases. Single haplotypes provide useful information for these studies but extracting single haplotypes directly by biochemical methods is expensive. A computational method to infer haplotypes from genotype data is therefore important. We investigate the problem of computing the minimum number of recombination events for general pedigrees with two sites for all members.ResultsWe show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem and therefore can be solved by an O(2k · n2) exact algorithm, where n is the number of members and k is the number of recombination events.ConclusionsOur work can therefore be useful for genetic disease studies to track down how changes in haplotypes such as recombinations relate to genetic disease.

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A Near-Linear Time Algorithm for Haplotype Determination on General Pedigrees

Cited by 3 publications

References 13 publications

An FPT haplotyping algorithm on pedigrees with a small number of sites

An FPT haplotyping algorithm on pedigrees with a small number of sites

A linear-time algorithm for reconstructing zero-recombinant haplotype configuration on a pedigree

Haplotype inference in general pedigrees with two sites

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