Efficient minimizer orders for large values ofkusing minimum decycling sets

Abstract

Minimizers are ubiquitously used in data structures and algorithms for efficient searching, mapping, and indexing of high-throughput DNA sequencing data. Minimizer schemes select a minimumk-mer in everyL-long subsequence of the target sequence, where minimality is with respect to a predefinedk-mer order. Commonly used minimizer orders select morek-mers than necessary and therefore provide limited improvement in runtime and memory usage of downstream analysis tasks. The recently introduced universalk-mer hitting sets produce minimizer orders with fewer selectedk-mers. Generating compact universalk-mer hitting sets is currently infeasible fork> 13, and thus, they cannot help in the many applications that require minimizer orders for largerk. Here, we close the gap of efficient minimizer orders for large values ofkby introducingdecycling-set-based minimizer orders: new minimizer orders based on minimum decycling sets. We show that in practice these new minimizer orders select a number ofk-mers comparable to that of minimizer orders based on universalk-mer hitting sets and can also scale to a largerk. Furthermore, we developed a method that computes the minimizers in a sequence on the fly without keeping thek-mers of a decycling set in memory. This enables the use of these minimizer orders for any value ofk. We expect the new orders to improve the runtime and memory usage of algorithms and data structures in high-throughput DNA sequencing analysis.