Perfect Phylogeny Haplotyping

Years and Authors of Summarized Original Work

• 2005; Ding, Filkov, Gusfield

Problem Definition

In the context of the perfect phylogeny haplotyping (PPH) problem, each vector ${ h\in \{0,1\}^m }$ is called a haplotype, while each vector ${ g\in \{0,1,2\}^m }$ is called a genotype. Haplotypes are binary encodings of DNA sequences, while genotypes are ternary encodings of pairs of DNA sequences (one sequence for each of the two homologous copies of a certain chromosome).

Two haplotypes ${ h^{\prime} }$ and ${ h^{\prime\prime} }$ are said to resolve a genotype g if, at each position j: (i) if ${ g_j\in \{0,1\} }$ then both ${ h^{\prime}_j = g_j }$ and ${ h^{\prime\prime}_{j}=g_j }$; (ii) if ${ g_j=2 }$ then either ${ h^{\prime}_j = 0 }$ and ${ h^{\prime\prime}_{j}=1 }$ or ${ h^{\prime}_j = 1 }$ and ${ h^{\prime\prime}_{j}=0 }$. If ${ h^{\prime} }$ and ${ h^{\prime\prime} }$ resolve g, we write ${ g = h^{\prime} + h^{\prime\prime} }$...