Haplotypic information in diploid organisms provides valuable information on human evolutionary history and plays an important role in identifying a candidate gene in the etiology of complex genetic diseases. However, haplotypes of diploid individuals cannot be acquired easily. Molecular haplotyping methods are very costly and have low throughput, and current genotyping and sequencing methods do not provide information on the linkage phase in diploid organisms. The application of statistical methods to infer the haplotype phase in samples of diploid sequences is a very cost-effective approach. Several computational and statistical methods have been developed for haplotype inference, including Clark's algorithm 1, the Expectation Maximization (EM) algorithm 2, and Gibbs sampler 3. Because of its interpretability and stability, the EM algorithm has become one of the most widely used statistical algorithms. However, the standard EM algorithm has several weaknesses, including the inability to handle a large number of markers and convergence to the local optimum. To overcome these problems, various derivative methods have been developed, such as the Partition-Ligation EM (PLEM) algorithm to handle many more linked loci 4, the Optimal Step Length EM (OSLEM) algorithm to accelerate the calculations 5, and the Stochastic EM (SEM) algorithm to deal with missing genotypic data and to avoid convergence to local maxima 6. However, most packages are intended for use with single-nucleotide polymorphism (SNP) data in a biallelic manner.

More and more researchers are analyzing both multiallelic and biallelic markers in the linkage and/or association studies of complex diseases. The analysis of linkage disequilibrium (LD) between multiallelic loci and haplotype inference of many loci (including bi- and multi-allelic markers) present a number of common problems. The major difficulty for the haplotype inference problem is exploring the large number of haplotype pairs that are consistent with the observed genotypes. One solution is to limit the number of candidate haplotypes. Ideally, a condensed haplotype set would make the process of haplotype inference quick and accurate. Our approach is to construct the haplotype space gradually rather than beginning with the set of all possible haplotypes.

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