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 sub-sequence of the target sequence, where minimality is with respect to a predefinedk-mer order. Commonly used minimizer orders select morek-mers overall than necessary and therefore provide limited improvement to runtime and memory usage of downstream analysis tasks. The recently introduced universalk-mer hitting sets produce minimizer orders resulting in fewer selectedk-mers. Unfortunately, generating compact universalk-mer hitting sets is currently infeasible fork >13, and thus cannot help in the many applications that need minimizers of largerk.Here, we close this gap by introducingdecycling set-based minimizer orders. We define new orders based on minimum decycling sets, which are guaranteed to hit any infinitely long sequence. 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 up to largerk. Furthermore, we developed a query method that avoids the need to keep thek-mers of a decycling set in memory, which enables the use of these minimizer orders for any value ofk. We expect the new decycling set-based minimizer orders to improve the runtime and memory usage of algorithms and data structures in high-throughput DNA sequencing analysis.

K2R: Tinted de Bruijn Graphs implementation for efficient read extraction from sequencing datasets

“…Through the application of “random minimizers”, which employ a hashing function, it is estimated that the number of selected minimizers required is twice the minimal theoretical number. Nevertheless, by adopting advanced minimizer selection algorithms [41, 31], onecan surpass these expectations and further reduce the number of selected minimizers in practice.…”

“…Recent advancements in minimizer selection techniques aim to closely approach this theoretical lower bound, thus reducing the quantity of necessary minimizers. We employ decycling set minimizers [31], which minimize the count of selected minimizers, albeit at the cost of increased computational overhead.…”

k-nonical space: sketching with reverse complements

“…This union function is not entirely new. Although motivated by a different goal, it is suggested in [18] to use an order for minimizers which is based on the set φ u , where φ is the Mykkeltveit set.…”

“…The Mykkeltveit and Champarnaud sets are two known construction methods for decycling sets of minimum size. Although these sets are not used on their own as sketching methods, the Mykkeltveit set in particular has been used as a starting point to define sketching methods [17, 16, 5, 18]. By construction, these sets are decycling.…”