Minimizer Density Revisited: Models and Multiminimizers.

Abstract

High-throughput sequence analysis commonly relies on k-mers and sampling schemes to improve scalability and data locality. Among these, local schemes are widely used and are typically evaluated by their density, the expected fraction of selected positions. Minimizers are the most common example, but recent near-tight lower bounds suggest diminishing room for improvement under the classical notion of density. Here, we revisit density and broaden its scope. First, we establish a direct link between density and the distance between consecutive selected positions. Under the sole assumption that these distances are identically distributed, we show that density is exactly the inverse of their expected distance, without assumptions on the selection mechanism. This provides a new way to analyze schemes beyond classical local models. Second, we introduce multiminimizers, a meta-scheme combining N minimizer schemes and selecting the candidate whose extends farthest. Multiminimizers are not local schemes, but under independent random component orders and locally distinct m-mers, their expected density converges exponentially to the optimum. Experiments with random minimizers and open-closed mod-minimizers confirm a controllable computation-density trade-off. Third, we introduce deduplicated density, measuring the fraction of distinct minimizers needed to cover all k-mers in a sequence set. We show that multiminimizers also improve this metric, prove that global optimization is NP-complete, and propose an effective local heuristic. Finally, we provide an efficient SIMD-accelerated Rust implementation and demonstrate reduced memory usage on core sequence-analysis tasks.