Pure Parsimony Xor Haplotyping
The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies . The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper we propose a formulation based on a well known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial-time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Moreover we propose a heuristic and produce an experimental analysis showing that it scales to real-world instances taken from the HapMap project.
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