Publications---ZRHC

Fast Elimination of Redundant Linear Equations and Reconstruction of Recombination-Free Mendelian Inheritance on a Pedigree.

By Jing Xiao, Lan Liu, Lirong Xia, and Tao Jiang.

Published in Proceedings of the ACM/SIAM Symposium on Discrete Algorithms (SODA-07), pp 655-664, 2007.

Abstract

Computational inference of haplotypes from genotypes has attracted a great deal of attention in the computational biology community recently, partially driven by the international HapMap project. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree, assuming that the hereditary process was free of mutations ( i.e. the Mendelian law of inheritance) and recombinants. The problem has recently been formulated as a system of linear equations over the finite field

of and solved in

time by using standard Gaussian elimination, where

is the number of loci (or markers) in a genotype and

the number of individuals in the pedigree. We give a much faster algorithm with running time

. The key ingredients of our construction are (i) a new system of linear equations based on some spanning tree of the pedigree graph and (ii) an efficient method for eliminating redundant equations in a system of

linear equations over

variables. Although such a fast elimination method is not known for general systems of linear equations, we take advantage of the underlying pedigree graph structure and recent progress on low-stretch spanning trees.

Paper

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