A Practical Parameterized Algorithm for Weighted Minimum Letter Flips Model of the Individual Haplotyping Problem

Given a set of DNA sequence fragments of an individual with each base of every fragment attached a confidence value, the weighted minimum letter flips model (WMLF) of the individual haplotyping problem is to infer a pair of haplotypes by flipping a number of bases such that the sum of the confidence values corresponding to the flipped bases is minimized. WMLF is NP-hard. This paper proposes a parameterized exact algorithm for WMLF of time $O(nk_22^{k_2}+mlogm+mk_1)$, where mis the number of fragments, nis the number of SNP sites, k 1 is the maximum number of SNP sites that a fragment covers, and k 2 is the maximum number of fragments that cover a SNP site. Since in real biological experiments, both k 1 and k 2 are small, the parameterized algorithm is efficient in practical application.

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