Abstract
In recent years, there has been a renewed interest in the search for low density minimizer schemes. These schemes take a window of $w$ consecutive $k$-mers, and sample one of them: the smallest under some specific order. Schemes such as the mod-minimizer provide a low density (fraction of sampled $k$-mers) when $k \gg w$, while schemes such as the greedy minimizer work well for explicit small parameters roughly in the regime $k \leq 2w$, for $k$ and $w$ up to $15$ or so. When $k 15\%$ above it. For alphabet size $\sigma=2$, the density is at most $10\%$ above the lower bound, which again improves over the $>50\%$ overhead of bd-anchors.