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We consider a combinatorial problem derived from haplotyping a population with respect to a genetic disease, either recessive or dominant. Given a set of individuals, partitioned into healthy and diseased, and the corresponding sets of genotypes, we want to infer ``bad'' and ``good'' haplotypes to account for these genotypes and for the disease. Assume e.g. the disease is recessive. Then, the resolving haplotypes must consist of \emph{bad} and \emph{good} haplotypes, so that (i) each genotype belonging to a diseased individual is explained by a pair of bad haplotypes and (ii) each genotype belonging to a healthy individual is explained by a pair of haplotypes of which at least one is good. We prove that the associated decision problem is NP-complete. However, we also prove that there is a simple solution, provided the data satisfy a very weak requirement.
Combinatorics, Discrete Mathematics, Biology and genetics
Romeo Rizzi, Giuseppe Lancia, R. Ravi, "Haplotyping for Disease Association: A Combinatorial Approach", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 5, no. , pp. 245-251, April-June 2008, doi:10.1109/TCBB.2007.70255
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