Efficient Algorithms for Reconstructing Zero-Recombinant Haplotypes on a Pedigree Based on Fast Elimination of Redundant Linear Equations

Xiao, Jing; Liu, Lan; Xia, Lirong; Jiang, Tao

doi:10.1137/070687591

Cited by 10 publications

(18 citation statements)

References 18 publications

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“…A preliminary test revealed that PedPhase terminated without giving a solution or giving an error message on a significant subset of instances and we preferred to not include it in this comparison. MePhase is a heuristic algorithm for the haplotype configuration with mutation and errors problem on tree pedigrees (i.e., pedigrees such that each pair of individuals are connected by at most one directed path) and it is based on an ILP formulation derived from a system of linear equations over Z 2 [15]. This formulation of the HI problem asks for a haplotype configuration of a given genotyped pedigree allowing mutations, genotyping errors, and missing genotypes, while in this work we allow recombinations, genotyping errors, and missing genotypes.…”

Section: Resultsmentioning

confidence: 99%

A fast and practical approach to genotype phasing and imputation on a pedigree with erroneous and incomplete information

Pirola

Vedova

Biffani³

et al. 2012

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Abstract. The Minimum-Recombinant Haplotype Configuration problem (MRHC) has been highly successful in providing a sound combinatorial formulation for the important problem of genotype phasing on pedigrees. Despite several algorithmic advances and refinements that led to some efficient algorithms, its applicability to real datasets has been limited by the absence of some important characteristics of these data in its formulation, such as mutations, genotyping errors, and missing data. In this work, we propose the Haplotype Configuration with Recombinations and Errors problem (HCRE), which generalizes the original MRHC formulation by incorporating the two most common characteristics of real data: errors and missing genotypes (including untyped individuals). Although HCRE is computationally hard, we propose an exact algorithm for the problem based on a reduction to the wellknown Satisfiability problem. Our reduction exploits recent progresses in the constraint programming literature and, combined with the use of state-of-the-art SAT solvers, provides a practical solution for the HCRE problem. Biological soundness of the phasing model and effectiveness (on both accuracy and performance) of the algorithm are experimentally demonstrated under several simulated scenarios and on a real dairy cattle population.

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Section: Resultsmentioning

confidence: 99%

A fast and practical approach to genotype phasing and imputation on a pedigree with erroneous and incomplete information

Pirola

Vedova

Biffani³

et al. 2012

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…The heuristic algorithm in [25] runs for days on a PC even for medium-sized datasets. Hence, recent work on MRHC has been focused on the special case where the number of recombinants is zero, the so called zero-recombinant haplotype configuration (ZRHC) problem [5,16,20,21,23,28,30,31]. In particular, Li and Jiang [16] formulated ZRHC as a system of linear equations over the field F (2) and devised an O(m 3 n 3 ) time algorithm using Gaussian elimination, where m is the number of loci and n is the size of the input pedigree.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, Li and Jiang [16] formulated ZRHC as a system of linear equations over the field F (2) and devised an O(m 3 n 3 ) time algorithm using Gaussian elimination, where m is the number of loci and n is the size of the input pedigree. Xiao et al [30,31] improved the running time to O(mn 2 + n 3 log 2 n log log n) by using a compact system of linear equations, taking advantage of some special properties of a pedigree graph, and the low-stretch spanning tree technique. The recent results in [5,20,21] presented linear (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Although ZRHC (or 0-RHC) seems easy to solve [5,20,21,30,31], the general k-RHC problem remains very hard to tackle. Observe that, we could obtain a trivial algorithm for k-RHC with time complexity O((mn) k (mn 2 + n 3 log 2 n log log n)) by using the algorithm in [30,31] for ZRHC and exhaustively enumerating the possible locations of the k recombinants. This is because the k-RHC instance can be easily transformed into a ZRHC instance once the recombinant locations are known.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Algorithm for Haplotype Inference on Pedigrees with a Small Number of Recombinants

2011

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Combinatorial (or rule-based) methods for inferring haplotypes from genotypes on a pedigree have been studied extensively in the recent literature. These methods generally try to reconstruct the haplotypes of each individual so that the total number of recombinants is minimized in the pedigree. The problem is NP-hard, although it is known that the number of recombinants in a practical dataset is usually very small. In this paper, we consider the question of how to efficiently infer haplotypes on a large pedigree when the number of recombinants is bounded by a small constant, i.e. the so called k-recombinant haplotype configuration (k-RHC) problem. We introduce a simple probabilistic model for k-RHC where the prior haplotype probability of a founder and the haplotype transmission probability from a parent to a child are all assumed to follow the uniform distribution and k random recombination events are assumed to have taken place uniformly and independently in the pedigree. We present an O(mn log k+1 n) time algorithm for k-RHC on tree pedigrees without mating loops, where m is the number of loci and n is the size of the input pedigree, and prove that when 90 log n < m < n 3 , the algorithm can correctly find a feasible haplotype configuration that obeys the Mendelian law of inheritance and requires no more than k recombinants with probability 1 − O(k 2 log 2 n mn + 1 n 2 ). The algorithm is efficient when k is of a moderate value and could thus be used to infer haplotypes from genotypes on large tree pedigrees efficiently in practice. We have implemented the algorithm as a C++ program named TREE-k-RHC. The implementation incorporates several ideas for dealing with missing data and data with a large number of recombinants effectively. Our experimental results on both simulated and real datasets show that TREE-k-RHC can reconstruct haplotypes with a high accuracy and is much faster than the best combinatorial method in the literature.

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“…Recent contributions include fine-scale recombination maps in humans [1], regions linked to Schizophrenia that might be missed by genome-wide association studies [2], and insights into the relationship between cystic fibrosis and fertility [3]. Algorithms for pedigree problems are of great interest to the computer science community, in part because of connections to machine learning algorithms, optimization methods, and combinatorics [4][5][6][7][8].…”

mentioning

confidence: 99%

Haplotypes versus Genotypes on Pedigrees

Kirkpatrick

2010

Lecture Notes in Computer Science

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Background: Genome sequencing will soon produce haplotype data for individuals. For pedigrees of related individuals, sequencing appears to be an attractive alternative to genotyping. However, methods for pedigree analysis with haplotype data have not yet been developed, and the computational complexity of such problems has been an open question. Furthermore, it is not clear in which scenarios haplotype data would provide better estimates than genotype data for quantities such as recombination rates.

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Efficient Algorithms for Reconstructing Zero-Recombinant Haplotypes on a Pedigree Based on Fast Elimination of Redundant Linear Equations

Cited by 10 publications

References 18 publications

A fast and practical approach to genotype phasing and imputation on a pedigree with erroneous and incomplete information

A fast and practical approach to genotype phasing and imputation on a pedigree with erroneous and incomplete information

An Efficient Algorithm for Haplotype Inference on Pedigrees with a Small Number of Recombinants

Haplotypes versus Genotypes on Pedigrees

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