The Haplotyping problem: An overview of computational models and solutions

Bonizzoni, Paola; Vedova, Gianluca Della; Dondi, Riccardo; Li, Jing

doi:10.1007/bf02945456

Cited by 111 publications

(75 citation statements)

References 20 publications

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“…Several optimization objectives have been considered for PHP and the related genotype phasing problem, which seeks a pair of haplotypes explaining each of the given genotypes -see, e.g., [3][4][5] for recent surveys. In the maximum likelihood approach to PHP, one assumes an a priori probability p h for every possible haplotype h (inferred, e.g., from genotype frequencies [6]), and seeks the most likely set H of haplotypes explaining the observed genotypes, where the likelihood of a set H is given by L(H) = h∈H p h .…”

Section: Maximum Likelihood Population Haplotypingmentioning

confidence: 99%

Minimum Multicolored Subgraph Problem in Multiplex PCR Primer Set Selection and Population Haplotyping

Hajiaghayi¹,

Jain

Lau

et al. 2006

Computational Science – ICCS 2006

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Abstract. In this paper we consider the minimum weight multicolored subgraph problem (MWMCSP), which is a common generalization of minimum cost multiplex PCR primer set selection and maximum likelihood population haplotyping. In this problem one is given an undirected graph G with non-negative vertex weights and a color function that assigns to each edge one or more of n given colors, and the goal is to find a minimum weight set of vertices inducing edges of all n colors. We obtain improved approximation algorithms and hardness results for MWMCSP and its variant in which the goal is to find a minimum number of vertices inducing edges of at least k colors for a given integer k ≤ n.

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Section: Maximum Likelihood Population Haplotypingmentioning

confidence: 99%

Minimum Multicolored Subgraph Problem in Multiplex PCR Primer Set Selection and Population Haplotyping

Hajiaghayi¹,

Jain

Lau

et al. 2006

Computational Science – ICCS 2006

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“…The M P P H problem, however, has so far hardly been studied beyond an NPhardness result [2] and occasional comments within P H and PPH literature [4][18] [19]. In this paper we thus provide what is one of the first attempts to analyse the parsimony optimisation criteria within a well-defined and widely applicable biological framework.…”

Section: Problem: Parsimony Haplotyping (P H)mentioning

confidence: 99%

Beaches of Islands of Tractability: Algorithms for Parsimony and Minimum Perfect Phylogeny Haplotyping Problems

Iersel

Keijsper

Kelk

et al. 2006

Lecture Notes in Computer Science

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The problem Parsimony Haplotyping (P H) asks for the smallest set of haplotypes which can explain a given set of genotypes, and the problem Minimum Perfect Phylogeny Haplotyping (M P P H) asks for the smallest such set which also allows the haplotypes to be embedded in a perfect phylogeny evolutionary tree, a well-known biologically-motivated data structure. For P H we extend recent work of [16] by further mapping the interface between "easy" and "hard" instances, within the framework of (k, l)-bounded instances. By exploring, in the same way, the tractability frontier of M P P H we provide the first concrete, positive results for this problem, and the algorithms underpinning these results offer new insights about how M P P H might be further tackled in the future. In both P H and M P P H intriguing open problems remain.

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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%

“…Let x and y be their neighbours via these edges, respectively. Then, in the branch where u is included in N , its neighbour x has to be inserted into C. Analogously, in the other branch, y has to be inserted into C. 3 Now assume that u has a neighbour x via a negative edge and v has a neighbour y via a negative edge. Analogously as in the preceding case, if u is included in C, then x has to be in N , and if v is included in C, then y has to be in N .…”

Section: If There Exists An Unassigned Vertex Vmentioning

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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The Haplotyping problem: An overview of computational models and solutions

Cited by 111 publications

References 20 publications

Minimum Multicolored Subgraph Problem in Multiplex PCR Primer Set Selection and Population Haplotyping

Minimum Multicolored Subgraph Problem in Multiplex PCR Primer Set Selection and Population Haplotyping

Beaches of Islands of Tractability: Algorithms for Parsimony and Minimum Perfect Phylogeny Haplotyping Problems

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

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