Algorithms for sparse Gaussian elimination with partial pivoting
ACM Transactions on Mathematical Software (TOMS)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Haplotyping as perfect phylogeny: conceptual framework and efficient solutions
Proceedings of the sixth annual international conference on Computational biology
Multilocus linkage analysis by blocked Gibbs sampling
Statistics and Computing
The Haplotyping problem: an overview of computational models and solutions
Journal of Computer Science and Technology
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
The complexity of checking consistency of pedigree information and related problems
Journal of Computer Science and Technology - Special issue on bioinformatics
A note on the single genotype resolution problem
Journal of Computer Science and Technology
Complexity and approximation of the minimum recombinant haplotype configuration problem
Theoretical Computer Science
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Family trio phasing and missing data recovery
International Journal of Bioinformatics Research and Applications
Linear-Time haplotype inference on pedigrees without recombinations
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
Solving haplotype inference problem with non-genotyped founders via integer linear programming
Journal of Combinatorial Optimization
Complexity and approximation of the minimum recombination haplotype configuration problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
On counting the number of consistent genotype assignments for pedigrees
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
k-Recombination haplotype inference in pedigrees
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Phasing and missing data recovery in family trios
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Fixed-parameter algorithm for general pedigrees with a single pair of sites
ISBRA'10 Proceedings of the 6th international conference on Bioinformatics Research and Applications
Efficient Genotype Elimination via Adaptive Allele Consolidation
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We study haplotype reconstruction under the Mendelian law of inheritance and the minimum recombination principleon pedigree data. We prove that the problem of finding a mini-mum-recombinant haplotype configuration (MRHC) is in general NP-hard. This is the first complexity result concerning the problem to our knowledge. An iterative algorithm based on blocks of consecutive resolved marker loci (called block-extension) is proposed. It is very efficient and can be used for large pedigrees with a large number of markers, especially for those data sets requiring few recombinants (or recombination events). A polynomial-time exact algorithm for haplotype reconstruction without recombinants is also presented. This algorithm first identifies all the necessary constraints based on the Mendelian law and the zero recombinant assumption, and represents them using a system of linear equations over the cyclic group Z2. By using a simple method based on Gaussian elimination, we could obtain all possible feasible haplotype configurations. We have tested the block-extension algorithm on simulated data generated on three pedigree structures. The results show that the algorithm performs very well on both multi-allelic and biallelic data, especially when the number of recombinants is small.