SNPs Problems, Complexity, and Algorithms

Lancia, Giuseppe; Bafna, Vineet; Istrail, Sorin; Lippert, Ross A.; Schwartz, Russell

doi:10.1007/3-540-44676-1_15

Cited by 171 publications

(201 citation statements)

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“…Reads (also called fragments) have to be assigned to the unknown haplotypes, using a reference genome in a preliminary mapping phase, if available. This involves dealing in some way with sequencing and mapping errors and leads to a computational task that is generally modelled as an optimization problem (Lancia et al, 2001;Lippert et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

HapCol: accurate and memory-efficient haplotype assembly from long reads

et al. 2015

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Motivation: Haplotype assembly is the computational problem of reconstructing haplotypes in diploid organisms and is of fundamental importance for characterizing the effects of single-nucleotide polymorphisms on the expression of phenotypic traits. Haplotype assembly highly benefits from the advent of 'future-generation' sequencing technologies and their capability to produce long reads at increasing coverage. Existing methods are not able to deal with such data in a fully satisfactory way, either because accuracy or performances degrade as read length and sequencing coverage increase or because they are based on restrictive assumptions. Results: By exploiting a feature of future-generation technologies-the uniform distribution of sequencing errors-we designed an exact algorithm, called HAPCOL, that is exponential in the maximum number of corrections for each single-nucleotide polymorphism position and that minimizes the overall error-correction score. We performed an experimental analysis, comparing HAPCOL with the current state-of-the-art combinatorial methods both on real and simulated data. On a standard benchmark of real data, we show that HAPCOL is competitive with state-of-the-art methods, improving the accuracy and the number of phased positions. Furthermore, experiments on realistically simulated datasets revealed that HAPCOL requires significantly less computing resources, especially memory. Thanks to its computational efficiency, HAPCOL can overcome the limits of previous approaches, allowing to phase datasets with higher coverage and without the traditional all-heterozygous assumption.

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Section: Introductionmentioning

confidence: 99%

HapCol: accurate and memory-efficient haplotype assembly from long reads

et al. 2015

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“…In particular, the problem of haplotyping a population (i.e., a set of individuals) has been extensively studied, under many objective functions [4,5,3], while haplotyping for a single individual has been studied in [8] and in [9].…”

Section: Introductionmentioning

confidence: 99%

“…the Minimum Fragment Removal (MFR) and the Minimum SNP Removal (MSR), are considered. The Haplotyping Problem was introduced in [8], where it was proved that both MSR and MFR are polynomially solvable when each fragment covers a set of consecutive SNPs (i.e., it is a gapless fragment), and NPhard in general. The original algorithms of [8] are of theoretical interest, but by no means practical.…”

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confidence: 99%

“…The Haplotyping Problem was introduced in [8], where it was proved that both MSR and MFR are polynomially solvable when each fragment covers a set of consecutive SNPs (i.e., it is a gapless fragment), and NPhard in general. The original algorithms of [8] are of theoretical interest, but by no means practical. In fact, one relies on finding the maximum stable set in a perfect graph, and the other is a reduction to a network flow problem.…”

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Practical Algorithms and Fixed-Parameter Tractability for the Single Individual SNP Haplotyping Problem

Rizzi

Bafna²,

Istrail³

et al. 2002

Lecture Notes in Computer Science

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Abstract. Single nucleotide polymorphisms (SNPs) are the most frequent form of human genetic variation, of foremost importance for a variety of applications including medical diagnostic, phylogenies and drug design. The complete SNPs sequence information from each of the two copies of a given chromosome in a diploid genome is called a haplotype. The Haplotyping Problem for a single individual is as follows: Given a set of fragments from one individual's DNA, find a maximally consistent pair of SNPs haplotypes (one per chromosome copy) by removing data "errors" related to sequencing errors, repeats, and paralogous recruitment. Two versions of the problem, i.e. the Minimum Fragment Removal (MFR) and the Minimum SNP Removal (MSR), are considered. The Haplotyping Problem was introduced in [8], where it was proved that both MSR and MFR are polynomially solvable when each fragment covers a set of consecutive SNPs (i.e., it is a gapless fragment), and NPhard in general. The original algorithms of [8] are of theoretical interest, but by no means practical. In fact, one relies on finding the maximum stable set in a perfect graph, and the other is a reduction to a network flow problem. Furthermore, the reduction does not work when there are fragments completely included in others, and neither algorithm can be generalized to deal with a bounded total number of holes in the data. In this paper, we give the first practical algorithms for the Haplotyping Problem, based on Dynamic Programming. Our algorithms do not require the fragments to not include each other, and are polynomial for each constant k bounding the total number of holes in the data. For m SNPs and n fragments, we give an O(mn 2k+2 ) algorithm for the MSR problem, and an O(2 2k m 2 n + 2 3k m 3 ) algorithm for the MFR problem, when each fragment has at most k holes. In particular, we obtain an O(mn 2 ) algorithm for MSR and an O(m 2 n + m 3 ) algorithm for MFR on gapless fragments. Finally, we prove that both MFR and MSR are APX-hard in general.Research partially done while enjoying hospitality at BRICS,

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“…There has been extensive research on the computational problem of reconstructing a pair of haplotypes from the DNA reads of a diploid genome, and many combinatorial optimization models (Xie et al, 2010a;Browning and Browning, 2011) have been proposed, including MEC (minimum error correction) (Lippert et al, 2002), MFR (minimum fragment removal), MSR (minimum SNP removal) (Lancia et al, 2001), and two recent models MFC (maximum fragments cut) (Duitama et al, 2010) and BOP (balanced optimal partition) (Xie et al, 2012). Most of the above models and their extended versions are NP-hard (Bafna et al, 2005;Cilibrasi et al, 2007;Duitama et al, 2010), and their exact algorithms run in time exponential in at least one input parameter (Bafna et al, 2005;He et al, 2010;Xie et al, 2010bXie et al, , 2008Wang et al, 2010;Bonizzoni et al, 2015;Patterson et al, 2015;Pirola et al, 2015).…”

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H-PoP and H-PoPG: heuristic partitioning algorithms for single individual haplotyping of polyploids

et al. 2016

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Motivation: Some economically important plants including wheat and cotton have more than two copies of each chromosome. With the decreasing cost and increasing read length of next-generation sequencing technologies, reconstructing the multiple haplotypes of a polyploid genome from its sequence reads becomes practical. However, the computational challenge in polyploid haplotyping is much greater than that in diploid haplotyping, and there are few related methods. Results: This paper models the polyploid haplotyping problem as an optimal poly-partition problem of the reads, called the Polyploid Balanced Optimal Partition (PBOP) model. For the reads sequenced from a k -ploid genome, the model tries to divide the reads into k groups such that the difference between the reads of the same group is minimized while the difference between the reads of different groups is maximized. When the genotype information is available, the model is extended to the Polyploid Balanced Optimal Partition with Genotype constraint (PBOPG) problem. These models are all NP-hard. We propose two heuristic algorithms, H-PoP and H-PoPG, based on dynamic programming and a strategy of limiting the number of intermediate solutions at each iteration, to solve the two models, respectively. Extensive experimental results on simulated and real data show that our algorithms can solve the models effectively, and are much faster and more accurate than the recent state-of-the-art polyploid haplotyping algorithms. The experiments also show that our algorithms can deal with long reads and deep read coverage effectively and accurately. Furthermore, H-PoP might be applied to help determine the ploidy of an organism. Availability: https://github.com/MinzhuXie/H-PoPG Contact:

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SNPs Problems, Complexity, and Algorithms

Cited by 171 publications

References 5 publications

HapCol: accurate and memory-efficient haplotype assembly from long reads

HapCol: accurate and memory-efficient haplotype assembly from long reads

Practical Algorithms and Fixed-Parameter Tractability for the Single Individual SNP Haplotyping Problem

H-PoP and H-PoPG: heuristic partitioning algorithms for single individual haplotyping of polyploids

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