The phasing of heterozygous traits: Algorithms and complexity

Combinatorial haplotyping problems have received great attention in the past few years. We review their definitions and the main results that were obtained for their solution. Haplotyping problems require one to determine a set HH of binary vectors (called haplotypes  ) that explain a set of GG of ternary vectors (called genotypes  ). The number χ(G)χ(G) of haplotypes to choose from can be exponential with respect to the number of genotypes. We give an exact formula, based on the inclusion–exclusion principle, for determining χ(G)χ(G).