Efficient Haplotype Block Partitioning and Tag SNP Selection Algorithms under Various Constraints

Patterns of linkage disequilibrium plays a central role in genome-wide association studies aimed at identifying genetic variation responsible for common human diseases. These patterns in human chromosomes show a block-like structure, and regions of high linkage disequilibrium are called haplotype blocks. A small subset of SNPs, called tag SNPs, is sufficient to capture the haplotype patterns in each haplotype block. Previously developed algorithms completely partition a haplotype sample into blocks while attempting to minimize the number of tag SNPs. However, when resource limitations prevent genotyping all the tag SNPs, it is desirable to restrict their number. We propose two dynamic programming algorithms, incorporating many diversity evaluation functions, for haplotype block partitioning using a limited number of tag SNPs. We use the proposed algorithms to partition the chromosome 21 haplotype data. When the sample is fully partitioned into blocks by our algorithms, the 2,266 blocks and 3,260 tag SNPs are fewer than those identified by previous studies. We also demonstrate that our algorithms find the optimal solution by exploiting the nonmonotonic property of a common haplotype-evaluation function.