A graph coloring approach to family-based haplotype reconstruction

TL;DR

This paper introduces a novel, efficient graph coloring method for family-based haplotype reconstruction, leveraging edge constrained vertex coloring problems to achieve linear-time complexity in genetic analysis.

Contribution

The paper develops a new haplotype reconstruction approach based on ECVC problems, offering linear-time performance and novel properties for analyzing recombination-free genomic intervals.

Findings

Linear-time algorithm for ECVC problems

Efficient haplotype reconstruction method

Applicable to recombination-free genomic intervals

Abstract

Edge Constrained Vertex Coloring (ECVC) problems are defined on a finite multigraph, their solutions are characterized, and a linear time algorithm is given for solving $N$ ECVCs on the same underlying multigraph. Using ECVC problems we develop a novel family-based haplotype reconstruction method which has linear-time complexity in both number of markers and family size and has many other desirable properties. To do so, we define a multigraph given a genomic interval on which a family is recombination-free.