The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Opportunities for Combinatorial Optimization in Computational Biology
INFORMS Journal on Computing
An approximation algorithm for haplotype inference by maximum parsimony
Proceedings of the 2005 ACM symposium on Applied computing
Haplotyping Populations by Pure Parsimony: Complexity of Exact and Approximation Algorithms
INFORMS Journal on Computing
Haplotype inference by pure Parsimony
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
A linear-time algorithm for the perfect phylogeny haplotyping (PPH) problem
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
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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.