This covers, for example, local, forward, and minimizer schemes, the density of the random minimizer, and a number of theoretical results on the optimal asymptotic density of schemes as \(k\to\infty\) or \(w\to\infty\). Minimizer schemes are always forward, and thus we have the following hierarchy \[ \textrm{minimizer schemes} \subseteq \textrm{forward schemes} \subseteq \textrm{local schemes}. The density of any forward scheme equals its average particular density over all cyclic strings of order \(c=w+k\) for forward schemes and \(c=2w+k-2\) for local schemes.