A New Integer Programming Formulation for the Pure Parsimony Problem in Haplotype Analysis

We present a new integer programming formulation for the haplotype inference by pure parsimony (HIPP) problem. Unlike a previous approach to this problem [2], we create an integer program whose size is polynomial in the size of the input. This IP is substantially smaller for moderate-sized instances of the HIPP problem. We also show several additional constraints, based on the input, that can be added to the IP to aid in finding a solution, and show how to find which of these constraints is active for a given instance in efficient time. We present experimental results that show our IP has comparable success to the formulation of Gusfield [2] on moderate-sized problems, though it is is much slower. However, our formulation can sometimes solve substantially larger problems than are practical with Gusfield’s formulation.