For a proband A, (putative) surrogate parents are identified based on IBS sharing. Ideally, the surrogate parents can be separated into two groups, which correspond to surrogate fathers and surrogate mothers. However, determining which group is which is not necessary for the purpose of phasing. Group 1 shares haplotype H1 with the proband while Group 2 shares H2. For a SNP that is heterozygous in A, phase is determined if at least one of the surrogate parents is homozygous. For example, if a surrogate parent in Group 1 is homozygous for the major allele, then H1 has the major allele and H2 has the minor allele. Consider a SNP that is heterozygous for A and all of his surrogate parents. Its phase can still be determined as long as one of his surrogate relatives with Erdös distance higher than 1 is homozygous. For example, let B be a member of Group 1 and apart from H1, let H3 be the other haplotype she carries. Treating B as the proband, one group of her surrogate parents includes everyone in Group 1
