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Pure Parsimony Xor Haplotyping
"... The haplotype resolution from xorgenotype data has been recently formulated as a new model for genetic studies [2]. The xorgenotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper we propose a for ..."
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formulation based on a wellknown model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixedparameter algorithm for the general case. These results are based on some interesting combinatorial
A decomposition of the pure parsimony problem
 In Lecture Notes in Computer Science
, 2009
"... Abstract. We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call glattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the N ..."
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Abstract. We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call glattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the NPHard problem can be solved efficiently. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models. 1
Integer programming approaches to haplotype inference by pure parsimony
 IEEE/ACM Transactions on Computational Biology and Bioinformatics
, 2006
"... Abstract—In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield’s IP can be of exponential size in the worst case ..."
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Cited by 45 (2 self)
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Abstract—In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield’s IP can be of exponential size in the worst
Haplotype inference by pure parsimony via genetic algorithm
 Beijing World Publishing Corporation, Beijing, People Republic of China
, 1997
"... Abstract Haplotypes are specially important in the study of complex diseases since they contain more information about gene alleles than genotype data. However, getting haplotype data via experiments methods is techniquely difficult and expensive. Thus, haplotype inference through computational meth ..."
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methods is practical and attractive. There are several models for inferrings haplotype from population genotypes, of which we are interested in the pure parsimony model. This problem has been proved to be an NPhard problem, so the goal of this paper is to design a heuristic method to obtain good
Haplotype Inference by Pure Parsimony with Constraint Programming
, 2009
"... Haplotype inference by pure parsimony problem (HIPP) is a computational problem in bioinformatics. It is a relatively new NPhard problem and it has been thoroughly explored using integer programming, SATbased programming and answer set programming. The state of the art approach is the SATbased mo ..."
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Haplotype inference by pure parsimony problem (HIPP) is a computational problem in bioinformatics. It is a relatively new NPhard problem and it has been thoroughly explored using integer programming, SATbased programming and answer set programming. The state of the art approach is the SAT
TOWARD AN ALGEBRAIC UNDERSTANDING OF HAPLOTYPE INFERENCE BY PURE PARSIMONY
"... Haplotype inference by pure parsimony (HIPP) is known to be NPHard. Despite this, many algorithms successfully solve HIPP instances on simulated and real data. In this paper, we explore the connection between algebraic rank and the HIPP problem, to help identify easy and hard instances of the probl ..."
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Haplotype inference by pure parsimony (HIPP) is known to be NPHard. Despite this, many algorithms successfully solve HIPP instances on simulated and real data. In this paper, we explore the connection between algebraic rank and the HIPP problem, to help identify easy and hard instances
Labbé M: The pure parsimony haplotyping problem: Overview and computational advances
 Int Trans Oper Res
"... Haplotyping estimation from aligned Single Nucleotide Polymorphism (SNP) fragments has attracted more and more attention in the recent years due to its importance in analysis of many finescale genetic data. Its application fields range from mapping of complex disease genes to inferring population h ..."
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Cited by 4 (2 self)
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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 the one having minimal cardinality. Finding the minimal number of haplotypes necessary to explain a given set
1 TOWARD AN ALGEBRAIC UNDERSTANDING OF HAPLOTYPE INFERENCE BY PURE PARSIMONY
"... 1. INTRODUCTION Haplotype inference is the process of attempting to identify the chromosomal sequences that have given rise to a diploid population. Recently, this problem has become increasingly important, as researchers attempt to connect variations to inherited diseases. The simplest haplotype in ..."
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inference problem to describe is haplotype inference by pure parsimony (HIPP), introduced by Gusfield1. The goal is to identify a smallest set of haplotypes to explain a set of genotypes. This objective is partly justified by the observation, now made in several species2, 3, that in genomic regions under
Gaspero. Twolevel ACO for haplotype inference under pure parsimony
 In Ant Colony Optimization and Swarm Intelligence, 6th International Workshop, ANTS 2008, volume 5217 of Lecture Notes in Computer Science
, 2008
"... Abstract. Haplotype Inference is a challenging problem in bioinformatics that consists in inferring the basic genetic constitution of diploid organisms on the basis of their genotype. This information enables researchers to perform association studies for the genetic variants involved in diseases an ..."
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and the individual responses to therapeutic agents. A notable approach to the problem is to encode it as a combinatorial problem under certain hypotheses (such as the pure parsimony criterion) and to solve it using offtheshelf combinatorial optimization techniques. At present, the main methods applied to Haplotype
On a Divide and Conquer Approach for Haplotype Inference with Pure Parsimony
"... Abstract—The genotype of an individual consists of two DNA strands, where each strand, called a haplotype, is inherited from each parent. The haplotypes of an individual may differ from those of his/her parents due to mutations or crossovers. Those haplotypes and their differences are the genetic ba ..."
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computational methods for inferring haplotypes from genotypes is an important problem. Since this haplotype inference problem can have multiple solutions, solutions with as few haplotypes as possible are often sought, leading to the Haplotype Inference problem with Pure Parsimony (HIPP). We present a divide
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