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Published Online: 1 September 2016

On the Minimum Error Correction Problem for Haplotype Assembly in Diploid and Polyploid Genomes

Publication: Journal of Computational Biology
Volume 23, Issue Number 9


In diploid genomes, haplotype assembly is the computational problem of reconstructing the two parental copies, called haplotypes, of each chromosome starting from sequencing reads, called fragments, possibly affected by sequencing errors. Minimum error correction (MEC) is a prominent computational problem for haplotype assembly and, given a set of fragments, aims at reconstructing the two haplotypes by applying the minimum number of base corrections. MEC is computationally hard to solve, but some approximation-based or fixed-parameter approaches have been proved capable of obtaining accurate results on real data. In this work, we expand the current characterization of the computational complexity of MEC from the approximation and the fixed-parameter tractability point of view. In particular, we show that MEC is not approximable within a constant factor, whereas it is approximable within a logarithmic factor in the size of the input. Furthermore, we answer open questions on the fixed-parameter tractability for parameters of classical or practical interest: the total number of corrections and the fragment length. In addition, we present a direct 2-approximation algorithm for a variant of the problem that has also been applied in the framework of clustering data. Finally, since polyploid genomes, such as those of plants and fishes, are composed of more than two copies of the chromosomes, we introduce a novel formulation of MEC, namely the k-ploid MEC problem, that extends the traditional problem to deal with polyploid genomes. We show that the novel formulation is still both computationally hard and hard to approximate. Nonetheless, from the parameterized point of view, we prove that the problem is tractable for parameters of practical interest such as the number of haplotypes and the coverage, or the number of haplotypes and the fragment length.

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Published In

cover image Journal of Computational Biology
Journal of Computational Biology
Volume 23Issue Number 9September 2016
Pages: 718 - 736
PubMed: 27280382


Published in print: September 2016
Published online: 1 September 2016
Published ahead of print: 9 June 2016


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Paola Bonizzoni
Department of Computer Science (DISCO), University of Milano-Bicocca, Milan, Italy.
Riccardo Dondi
Department of Social and Human Sciences, University of Bergamo, Bergamo, Italy.
Gunnar W. Klau
Life Sciences Group, Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands.
ERABLE Team, INRIA, Lyon, France.
Yuri Pirola
Department of Computer Science (DISCO), University of Milano-Bicocca, Milan, Italy.
Nadia Pisanti
ERABLE Team, INRIA, Lyon, France.
Department of Computer Science, University of Pisa, Pisa, Italy.
Simone Zaccaria
Department of Computer Science (DISCO), University of Milano-Bicocca, Milan, Italy.


A preliminary version of this article partially appeared in Bonizzoni et al. (2015).
Address correspondence to:Dr. Paola BonizzoniDip. di Informatica Sistemistica e ComunicazioneUniv. degli Studi di Milano-BicoccaViale Sarca 336Milan 20126Italy
E-mail: [email protected]

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No competing financial interests exist.

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