Pure Parsimony Xor Haplotyping
Abstract
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. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given SNP. Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project.
Cite
@article{arxiv.1001.1210,
title = {Pure Parsimony Xor Haplotyping},
author = {Paola Bonizzoni and Gianluca Della Vedova and Riccardo Dondi and Yuri Pirola and Romeo Rizzi},
journal= {arXiv preprint arXiv:1001.1210},
year = {2013}
}