Density and Conservation Optimization of the Generalized Masked-Minimizer Sketching Scheme

Minimizers and syncmers are sketching methods that sample representative k-mer seeds from a long string. The minimizer scheme guarantees a well-spread k-mer sketch (high coverage) while seeking to minimize the sketch size (low density). The syncmer scheme yields sketches that are more robust to base substitutions (high conservation) on random sequences, but do not have the coverage guarantee of minimizers. These sketching metrics are generally adversarial to one another, especially in the context of sketch optimization for a specific sequence, and thus are difficult to be simultaneously achieved. The parameterized syncmer scheme was recently introduced as a generalization of syncmers with more flexible sampling rules and empirically better coverage than the original syncmer variants. However, no approach exists to optimize parameterized syncmers. To address this shortcoming, we introduce a new scheme called masked minimizers that generalizes minimizers in manner analogous to how parameterized syncmers generalize syncmers and allows us to extend existing optimization techniques developed for minimizers. This results in a practical algorithm to optimize the masked minimizer scheme with respect to both density and conservation. We evaluate the optimization algorithm on various benchmark genomes and show that our algorithm finds sketches that are overall more compact, well-spread, and robust to substitutions than those found by previous methods. Our implementation is released at https://github.com/Kingsford-Group/maskedminimizer. This new technique will enable more efficient and robust genomic analyses in the many settings where minimizers and syncmers are used.