Pure Parsimony Xor Haplotyping

TL;DR

This paper introduces a new model for haplotype inference from xor-genotype data using pure parsimony, providing exact algorithms, approximation methods, and a scalable heuristic validated on real-world data.

Contribution

It formulates xor-genotype haplotyping as a pure parsimony problem and offers polynomial algorithms for special cases, a fixed-parameter algorithm, and a scalable heuristic.

Findings

Exact polynomial-time algorithms for restricted cases

A polynomial-time k-approximation algorithm

A heuristic that scales to large real-world datasets

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.