Fig. 3.

Graph that represents the optimization problem of equation (1). An optimal solution for $(s_1,\dots ,s_p)$ is found by finding the shortest path from node a to node b. We assume that there are n individuals in the source populations resulting in 2n haplotypes denoted by $(H_1,\cdots ,H_{2n})$. The value (0 or 1) of the ith haplotype at the jth SNP is denoted by $H_i^j$. A vector $(s_1,\dots ,s_p)$ describes the sequence of haplotype labels from which the haplotype h of an admixed individual can be approximated. For the jth SNP in the data set, s_j = k if haplotype h results from a copy of haplotype H_k.