Figure 2
From: A novel approach for haplotype-based association analysis using family data
Illustration of the DSS algorithm. a) The input pedigree with 8 members and their genotype data. b) Haplotypes are partially determined based on the Mendelian law and denoted as (paternal | maternal). In addition, one heterozygous SNP is fixed in each founder (an individual without parents in the pedigree). Five SNPs are left with freedom. c) Locus graphs for the two loci. Each graph has the same set of nodes as the original pedigree, where shaded (predetermined) nodes representing fixed SNPs in b). Each child is linked to its heterozygous parents, with edges labeled using h-variables. Node 5 is duplicated for easy process. d) Left: constraints on h-variables collected based on the two locus graphs using disjoint-set structures. Constraints are collected based on each pair of linked predetermined nodes (or duplicated nodes), and only no redundant ones are kept. Right: Solutions of h-variables can be obtained directly based on the disjoint-set structures. They are represented by free variables α. In this example, only one degree of freedom. e) Solutions of p variables derived from h variables in d).