Haplotype Block Partitioning and tagSNP Selection under the Perfect Phylogeny Model

Single Nucleotide Polymorphisms (SNPs) are the most usual form of polymorphism in human genome.Analyses of genetic variations have revealed that individual genomes share common SNP-haplotypes. Theparticular pattern of these common variations forms a block-like structure on human genome. In this work,we develop a new method based on the Perfect Phylogeny Model to identify haplotype blocks usingsamples of individual genomes. We introduce a rigorous definition of the quality of the partitioning of haplotypes into blocks and devise a greedy algorithm for finding the proper partitioning in case of perfect andsemi-perfect phylogeny. It is shown that the minimum number of tagSNPs in a haplotype block of PerfectPhylogeny can be obtained by a polynomial time algorithm. We compare the performance of our algorithmon haplotype data of human chromosome 21 with other previously developed methods through simulations.The results demonstrate that our algorithm outperforms the conventional implementation of the FourGamete Test approach which is the only available method for haplotype block partitioning based onPerfect Phylogeny.