Solving haplotyping inference parsimony problem using a new basic polynomial formulation

Bertolazzi, Paola; Godi, Alessandra; Tininini, Leonardo

doi:10.1016/j.camwa.2006.12.095

Cited by 15 publications

(10 citation statements)

References 13 publications

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“…To minimize the number of distinct haplotypes, Brown and Harrower (2004) proposed constructing haplotype vectors by associating a variable to each site; they subsequently used constraints to establish the exact haplotype structures. On the other hand, Bertolazzi et al (2008) first formulated PPH as a minimization problem characterized by a polynomial number of variables and constraints. Then the authors turned the problem into a maximization problem and strengthened the model by using clique inequalities, symmetry breaking, inequalities, and dominance relations.…”

Section: Introductionmentioning

confidence: 99%

“…The author described a model, exponential in size, characterized by two kinds of variables-one for haplotypes and the other for haplotype pairs-and by the exhaustive generation of the set of all haplotypes compatible with some genotype in the input. Similar integer programming models were also used by Brown and Harrower (2004) and Bertolazzi et al (2008). To minimize the number of distinct haplotypes, Brown and Harrower (2004) proposed constructing haplotype vectors by associating a variable to each site; they subsequently used constraints to establish the exact haplotype structures.…”

Section: Introductionmentioning

confidence: 99%

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A Class Representative Model for Pure Parsimony Haplotyping

Catanzaro

Godi

2010

INFORMS Journal on Computing

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H aplotyping estimation from aligned single nucleotide polymorphism fragments has attracted increasing attention in recent years because of its importance in the analysis of fine-scale genetic data. Its application fields range from mapping of complex disease genes to inferring population histories, passing through designing drugs, functional genomics, and pharmacogenetics. The literature proposes several criteria for haplotyping populations, each of them characterized by biological motivations. One of the most important haplotyping criteria is parsimony, which consists of finding the minimum number of haplotypes necessary to explain a given set of genotypes. Parsimonious haplotype estimation is an -hard problem for which the literature has proposed several integer programming (IP) models. Here, we describe a new polynomial-sized IP model based on the concept of class representatives, already used for the coloring problem. We propose valid inequalities to strengthen our model and show, through computational experiments, that our model outperforms the best IP models currently known in literature.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Class Representative Model for Pure Parsimony Haplotyping

Catanzaro

Godi

2010

INFORMS Journal on Computing

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“…Such a sequence has the same allele on a site as the two (unknown) haplotype sequences if they agree on that site and otherwise is regarded as ambiguous. Combined with the fact that the determination of haplotype sequences via experiments is usually highly costly and time consuming [3], [4] it is therefore not surprising that the problem of inferring for a set of genotype sequences a set of, in a welldefined sense, explaining haplotype sequences has received a considerable amount of attention in the literature. For example, cast as a statistical problem it has led to powerful approaches such as PHASE [5] which have turned out to be particularly useful in case the amount of variability in a set of genotype sequences is high (see [6], [7] for more on this and [8] for a recent overview on statistical approaches).…”

Section: Introductionmentioning

confidence: 99%

A GRASP-based approach for the Pure Parsimony Haplotype Inference problem

Suchecki

Chardaire

Huber

2010

2010 2nd Computer Science and Electronic Engineering Conference (CEEC)

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The availability and study of haplotype data is of considerable interest to a wide range of areas including general health care, personalized medicine, and pharmacogenetics. The inner workings of contemporary sequencing techniques however imply that genotype data is generated from a chromosome rather than haplotype data. The reconstruction of the latter from this kind of data lies at the heart of the well studied Pure Parsimony Haplotype Inference problem (PPHI). In this paper, we present a proof of concept that a GRASP-based approach for solving PPHI has the potential of yielding an attractive tool that complements existing approaches. The usage of this strategy for solving PPHI is novel. To assess its suitability, we have implemented it in basic form in the novel and freely available HAPLOGRASP approach which we assessed in terms of simulated and real data. Our findings are highly encouraging.

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“…An alternative greedy heuristic, called Collaps, was proposed by Bertolazzi et al (2008). The idea at its core is based on the fact that any solution of PPH may be represented by means of a matrix H having at most 2m distinct rows and p columns.…”

Section: Approximation Algorithmsmentioning

confidence: 99%

“…Finally, constraints (36)- (39) impose the sum operator between haplotypes. Bertolazzi et al (2008) set the initial value of UB by means of a heuristic called Collaps (see Section 5.2). However, the authors observed that PPH can be solved by replacing Formulation 5 by a sequence of maximization problems.…”

Section: Polynomial and Hybrid Ilp Modelsmentioning

confidence: 99%

The pure parsimony haplotyping problem: overview and computational advances

Catanzaro

2009

Int Trans Operational Res

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Haplotyping estimation from aligned single-nucleotide polymorphism fragments has attracted more and more attention in recent years due to its importance in analysis of many fine-scale genetic data. Its application fields range from mapping of complex disease genes to inferring population histories, passing through designing drugs, functional genomics, and pharmacogenetics. The literature proposes a number of estimation criteria to select a set of haplotypes among possible alternatives. Usually, such criteria can be expressed under the form of objective functions, and the sets of haplotypes that optimize them are referred to as optimal. One of the most important estimation criteria is the pure parsimony, which states that the optimal set of haplotypes for a given set of genotypes is that having minimal cardinality. Finding the minimal number of haplotypes necessary to explain a given set of genotypes involves solving an optimization problem, called the pure parsimony haplotyping ( PPH) estimation problem, which is notoriously NP-hard. This article provides an overview of PPH, and discusses the different approaches to solution that occur in the literature.

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Solving haplotyping inference parsimony problem using a new basic polynomial formulation

Cited by 15 publications

References 13 publications

A Class Representative Model for Pure Parsimony Haplotyping

A Class Representative Model for Pure Parsimony Haplotyping

A GRASP-based approach for the Pure Parsimony Haplotype Inference problem

The pure parsimony haplotyping problem: overview and computational advances

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