GraphSlimmer: Preserving Read Mappability with the Minimum Number of Variants.

Modern genomic datasets, like those generated under the 1000 Genome Project, contain millions of variants belonging to known haplotypes. Although these datasets are more representative than a single reference sequence and can alleviate issues like reference bias, they are significantly more computationally burdensome to work with, often involving large-indexed genome graph data structures for tasks such as read mapping. The construction, preprocessing, and mapping algorithms can require substantial computational resources depending on the size of these variant sets. Moreover, the accuracy of mapping algorithms has been shown to decrease when working with complete variant sets. Therefore, a drastically reduced set of variants that preserves important properties of the original set is desirable. This work provides a technique for finding a minimal subset of variants $S$ such that for given parameters α and δ, all substrings up to length α in the haplotypes are guaranteed to be still alignable to the appropriate locations with either Hamming or edit distance at most δ, using only $S$. Our contributions include showing the NP-hardness and inapproximability of these optimization problems and providing Integer Linear Programming (ILP) formulations. Our edit distance ILP formulation carefully decomposes the problem according to variant locations, which allows it to scale to support all of chromosome 22's variants from the 1000 Genome Project. Our experiments also demonstrate a significant reduction in the number of variants. For example, for moderately long reads, e.g., α = 1000, over 75% of the variants can be removed while preserving read mappability with edit distance at most one.