Haplotyping as perfect phylogeny: conceptual framework and efficient solutions
Proceedings of the sixth annual international conference on Computational biology
A Practical Algorithm for Optimal Inference of Haplotypes from Diploid Populations
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
The Approximation of Maximum Subgraph Problems
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
SNPs Problems, Complexity, and Algorithms
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Journal of Computer and System Sciences
Haplotypes and informative SNP selection algorithms: don't block out information
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
The Haplotyping problem: an overview of computational models and solutions
Journal of Computer Science and Technology
Polynomial and APX-hard cases of the individual haplotyping problem
Theoretical Computer Science - Pattern discovery in the post genome
Haplotyping Populations by Pure Parsimony: Complexity of Exact and Approximation Algorithms
INFORMS Journal on Computing
Computational Biology and Chemistry
Planar graph bipartization in linear time
Discrete Applied Mathematics
Haplotype Assembly from Weighted SNP Fragments and Related Genotype Information
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Self-organizing map approaches for the haplotype assembly problem
Mathematics and Computers in Simulation
On the Approximability of Some Haplotyping Problems
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Haplotype assembly from aligned weighted SNP fragments
Computational Biology and Chemistry
Combinatorial problems arising in SNP and haplotype analysis
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Proceedings of the forty-second ACM symposium on Theory of computing
ReFHap: a reliable and fast algorithm for single individual haplotyping
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
An (almost) linear time algorithm for odd cycles transversal
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved exact exponential algorithms for vertex bipartization and other problems
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
On the complexity of several haplotyping problems
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Algorithm engineering for optimal graph bipartization
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
On polynomial kernels for structural parameterizations of odd cycle transversal
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Finding odd cycle transversals
Operations Research Letters
Using genetic algorithm in reconstructing single individual haplotype with minimum error correction
Journal of Biomedical Informatics
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
A heuristic algorithm for haplotype reconstruction from aligned weighted SNP fragments
International Journal of Bioinformatics Research and Applications
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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(mn2k+2) algorithm for the MSR problem, and an O(22km2n+23km3) algorithm for the MFR problem, when each fragment has at most k holes. In particular, we obtain an O(mn2) algorithm for MSR and an O(m2n+m3) algorithm for MFR on gapless fragments.Finally, we prove that both MFR and MSR are APX-hard in general.