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Issue No. 06 - November/December (2011 vol. 8)
ISSN: 1545-5963
pp: 1692-1699
Michael R. Fellows , The University of Newcastle, Newcastle
Tzvika Hartman , Google, Tel Aviv
Danny Hermelin , Max Planck Institute for Informatics, Saarbrucken
Gad M. Landau , University of Haifa, Haifa
Frances Rosamond , The University of Newcastle, Newcastle
Liat Rozenberg , University of Haifa, Haifa
The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of genetic mutations. In order to find the haplotypes which are as close as possible to the real set of haplotypes that comprise the genotypes, two models have been suggested which are by now well-studied: The perfect phylogeny model and the pure parsimony model. All known algorithms up till now for haplotype inference may find haplotypes that are not necessarily plausible, i.e., very rare haplotypes or haplotypes that were never observed in the population. In order to overcome this disadvantage, we study in this paper, a new constrained version of HIP under the above-mentioned models. In this new version, a pool of plausible haplotypes \widetilde{H} is given together with the set of genotypes G, and the goal is to find a subset H \subseteq \widetilde{H} that resolves G. For constrained perfect phylogeny haplotyping (CPPH), we provide initial insights and polynomial-time algorithms for some restricted cases of the problem. For constrained parsimony haplotyping (CPH), we show that the problem is fixed parameter tractable when parameterized by the size of the solution set of haplotypes.
Haplotyping, perfect phylogeny, pure parsimony, polynomial-time algorithms, parameterized complexity.

F. Rosamond, G. M. Landau, M. R. Fellows, D. Hermelin, T. Hartman and L. Rozenberg, "Haplotype Inference Constrained by Plausible Haplotype Data," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. , pp. 1692-1699, 2010.
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