SNPs problems, complexity, and algorithms

Single nucleotide polymorphisms (SNPs) are the most frequent form of human genetic variation. They are of fundamental importance for a variety of applications including medical diagnostic and drug design. They also provide the highest–resolution genomic fingerprint for tracking disease genes. This paper is devoted to algorithmic problems related to computational SNPs validation based on genome assembly of diploid organisms. In diploid genomes, there are two copies of each chromosome. A description of the SNPs sequence information from one of the two chromosomes is called SNPs haplotype. The basic problem addressed here is the Haplotyping, i.e., given a set of SNPs prospects inferred from the assembly alignment of a genomic region of a chromosome, find the maximally consistent pair of SNPs haplotypes by removing data "errors" related to DNA sequencing errors, repeats, and paralogous recruitment. In this paper, we introduce several versions of the problem from a computational point of view. We show that the general SNPs Haplotyping Problem is NP–hard for mate–pairs assembly data, and design polynomial time algorithms for fragment assembly data. We give a network–flow based polynomial algorithm for the Minimum Fragment Removal Problem, and we show that the Minimum SNPs Removal problem amounts to finding the largest independent set in a weakly triangulated graph.