Diploid organisms, such as humans, inherit one copy of each chromosome (haplotype) from each parent. The conflation of inherited haplotypes is called the genotype of the organism. In many disease association studies, the haplo-type data is more informative than the genotype data. Unfortunately, getting haplotype data experimentally is both expensive and difficult. The haplotype inference with pure parsimony (HPP) problem is the problem of finding a minimal set of haplotypes that resolve a given set of genotypes.

We provide a Quadratic Integer Programming (QIP) formulation for the HPP problem, and describe an algorithm for the HPP problem based on a semi-definite programming (SDP) relaxation of that QIP program. We compare our approach with existing approaches. Further, we show that the proposed approach is capable of incorporating a variety of additional constraints, such as missing or erroneous genotype data, outliers etc.