Algorithm for Haplotype Inference via Galled-Tree Networks with Simple Galls

The problem of determining haplotypes from genotypes has gained considerable prominence in the research community. Here the focus is on determining sets of SNP values on individual chromosomes since such information captures the genetic causes of diseases. The most efficient algorithmic tool for haplotyping is based on perfect phylogenetic trees. A drawback of this method is that it cannot be applied in situations when the data contains homoplasies (multiple mutations of the same character) or recombinations. Recently, Song et al. ( 2005 ) studied the two cases: haplotyping via imperfect phylogenies with a single homoplasy and via galled-tree networks with one gall. In Gupta et al. ( 2010 ), we have shown that the haplotyping via galled-tree networks is NP-hard, even if we restrict to the case when every gall contains at most 3 mutations. We present a polynomial algorithm for haplotyping via galled-tree networks with simple galls (each having two mutations) for genotype matrices which satisfy a natural condition which is implied by presence of at least one 1 in each column that contains a 2. In the end, we give the experimental results comparing our algorithm with PHASE on simulated data.

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