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 , 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  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.
KeywordsInteger Program Problem Instance Linear Program Relaxation Unique Haplotype Fractional Solution
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