Example: Fair coordinate schedules

On ${\mathbb{Z}}^D$ with the ${\ell }^1$ metric, define, along one coordinate axis, the two partitions with intervals

and singletons at all remaining sites. Lift these partitions along each coordinate line.

A schedule that repeats both phases on every axis is tail routing. Every nearest-neighbor edge lies in an interval of one of the two phases. A name can therefore follow any finite coordinate path by waiting for the required phase. Previously routed names may remain at the target while the remaining names are transported.