Haplotype inferring via galled-tree networks using a hypergraph covering problem for special genotype matrices

Since exact determination of haplotype blocks is usually not possible, it is desirable to develop a haplotyping method which can account for recombinations. A natural candidate for such a method is haplotyping via phylogenetic networks or their simplified version: galled-tree networks. In earlier work we characterized the existence of the galled-tree networks. Building on this, we reduce the problem of haplotype inferring via galled-tree networks to a hypergraph covering problem for genotype matrices satisfying a combinatorial condition. Our experiments on actual data show that this condition is almost always satisfied when the percentage of minor alleles for each SNP reaches at least 30%.