A Class Representative Model for Pure Parsimony Haplotyping

Haplotyping estimation from aligned Single Nucleotide Polymorphism (SNP) fragments has attracted more and more attention in the recent years due to its importance in analysis of many fine-scale genetic data. Its application fields range from mapping of complex disease genes to inferring population histories, passing through designing drugs, functional genomics and pharmacogenetics. The literature proposes several criteria for haplotyping populations, each of them characterized by biological motivations. One of the most important haplotyping criteria is the parsimony which consists of finding the minimum number of haplotypes necessary to explain a given set of genotypes. Parsimonious haplotype estimation is a NP-Hard problem for which the literature has proposed several Integer Programming (IP) models. Here we describe a new polynomial-sized IP model based on the concept of class representatives, already used for the coloring problem. We propose valid inequalities to strengthen our model and show, through computational experiments, that our model outperforms the best IP models currently known in literature.