A practical parameterized algorithm for the individual haplotyping problem MLF

The individual haplotyping problem Minimum Letter Flip (MLF) is a computational problem that, given a set of aligned DNA sequence fragment data of an individual, induces the corresponding haplotypes by flipping minimum SNPs. There has been no practical exact algorithm to solve the problem. In DNA sequencing experiments, due to technical limits, the maximum length of a fragment sequenced directly is about 1kb. In consequence, with a genome-average SNP density of 1.84 SNPs per 1 kb of DNA sequence, the maximum number k(1) of SNP sites that a fragment covers is usually small. Moreover, in order to save time and money, the maximum number k(2) of fragments that cover a SNP site is usually no more than 19. Based on the properties of fragment data, the current paper introduces a new parameterized algorithm of running time O(nk(2)2 (k2) + mlogm + mk(1)), where m is the number of fragments, n is the number of SNP sites. The algorithm solves the MLF problem efficiently even if m and n are large, and is more practical in real biological applications.