New results for the Longest Haplotype Reconstruction problem

The haplotyping problem has emerged in recent years as one of the most relevant problems in Computational Biology. In particular, in the Single Individual Haplotyping (SIH) problem, starting from a matrix of incomplete haplotype fragments, the goal is the reconstruction of the two complete haplotype...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 160; no. 9; pp. 1299 - 1310
Main Author: Dondi, Riccardo
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2012
Subjects:
Algorithms
Approximation
Approximation complexity
Biology
Computation
Computational biology
Fixed-parameter algorithms
Haplotyping
Mathematical analysis
Mathematical models
Reconstruction
Surface hardness
Haplotyping
Approximation complexity
Fixed-parameter algorithms
Computational biology
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:The haplotyping problem has emerged in recent years as one of the most relevant problems in Computational Biology. In particular, in the Single Individual Haplotyping (SIH) problem, starting from a matrix of incomplete haplotype fragments, the goal is the reconstruction of the two complete haplotypes of an individual. In this paper we consider one of the variants of the Single Individual Haplotyping problem, the Longest Haplotyping Reconstruction (LHR) problem. We prove that the LHR problem is NP-hard even in the restricted case when the input matrix is error-free. Furthermore, we investigate the approximation complexity of the problem, and we show that the problem cannot be approximated within factor 2logδnm for any constant δ<1, unless NP⊆DTIME[2polylognm]. Finally, we exhibit a fixed-parameter algorithm for the LHR problem, where the parameter is the size of the two reconstructed haplotypes.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2011.10.014