A Probabilistic Branch-and-Bound Approach for Reconstructing of Haplotype Using SNP-Fragments and Related Genotype

Most positions of the human genome are typically invariant (99%) and only some positions (1%) are commonly invariant which are associated with complex genetic diseases. Haplotype reconstruction problem divide aligned single nucleotide polymorphism (SNP) fragments into two classes and infer a pair of haplotypes from them. An important computational model of this problem is minimum error correction (MEC) but it is only effective when the error rate of the fragments is low. MEC/GI as an extension to MEC employs the compatible genotype information besides the SNP fragments and so results in a more accurate inference. The haplotyping problems, due to its NP-hardness, several computational and heuristic methods have addressed the problem seeking feasible answers. In this paper, we develop a new branch-and-bound algorithm with running time O([(n-h)/k]2ˆh x nm) in which m is maximum length of SNP fragments where SNP sites are heterozygous, n is the number of fragments and h is depth of our exploration in binary tree. Since h (h?n) is small in real biological applications, our proposed algorithm is practical and efficient.