Table of Contents The importance of ordering Asymptotically optimal minimizers These are some (biased) comments on “When Less Is More: Sketching with Minimizers in Genomics” (Ndiaye et al. 2024). The importance of ordering the interest lies in constructing a minimizer with a density within a constant factor, i.e., \(O(1/w)\) for any \(k\). With lexicographic ordering, minimizers can achieve such density, but with large \(k\) values (\(\geq \log_{|Σ|}(w)-c\) for a constant \(c\)), which m...
