Sequence-specific minimizers via polar sets

Abstract

AbstractMinimizers are efficient methods to samplek-mers from genomic sequences that unconditionally preserve sufficiently long matches between sequences. Well-established methods to construct efficient minimizers focus on sampling fewerk-mers on a random sequence and use universal hitting sets (sets ofk-mers that appear frequently enough) to upper bound the sketch size. In contrast, the problem of sequence-specific minimizers, which is to construct efficient minimizers to sample fewerk-mers on a specific sequence such as the reference genome, is less studied. Currently, the theoretical understanding of this problem is lacking, and existing methods do not specialize well to sketch specific sequences. We propose the concept of polar sets, complementary to the existing idea of universal hitting sets. Polar sets arek-mer sets that are spread out enough on the reference, and provably specialize well to specific sequences. Link energy measures how well spread out a polar set is, and with it, the sketch size can be bounded from above and below in a theoretically sound way. This allows for direct optimization of sketch size. We propose efficient heuristics to construct polar sets, and via experiments on the human reference genome, show their practical superiority in designing efficient sequence-specific minimizers. A reference implementation and code for analyses under an open-source license are athttps://github.com/kingsford-group/polarset.