Haplotype Inference Constrained by Plausible Haplotype Data

Abstract

Abstract. The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of genetic mutations. In order to find the haplotypes which are as close as possible to the real set of haplotypes that comprise the genotypes, two models have been suggested which are by now well-studied: The perfect phylogeny model and the pure parsimony model. All known algorithms up till now for haplotype inference may find haplotypes that are not necessarily plausible, i.e. very rare haplotypes or haplotypes that were never observed in the population. In order to overcome this disadvantage we study in this paper a new constrained version of HIP under the above mentioned models. In this new version, a pool of plausible haplotypes H is given together with the set of genotypes G, and the goal is to find a subset H ⊆ H that resolves G. For constrained perfect phylogeny haplotyping (CPPH), we provide initial insights and polynomial-time algorithms for some restricted cases of the problem. For constrained parsimony haplotyping (CPH), we show that the problem is fixed parameter tractable when parameterized by the size of the solution set of haplotypes.

Parameterized Algorithms in Bioinformatics: An Overview

“…Further special cases were considered by Sharan et al [125] who also presented an O(k k 2 +k m)-time algorithm for the general case [125]. A variant where haplotypes can only be picked from a prescribed pool H was considered by Fellows et al [129] who showed a O(k O(k 2 ) n 2 m)-time algorithm. Fleischer et al [130] later presented an O(k 4k+3 m)-time algorithm for the unconstrained version that can also solve the constraint version in O(k 4k+3 m|H | 2 ) time (indeed, these running times can be decreased to O(k 4k+2 m) and O(k 4k+2 m|H |) on average using perfect hashing) as well as a size-O(2 k k 2 ) kernel.…”