  In the rectilinear Steiner arborescence problem the task is to build a
shortest rectilinear Steiner tree connecting a given root and a set of
terminals which are placed in the plane such that all root-terminal-paths are
shortest paths. This problem is known to be NP-hard.
  In this paper we consider a more restricted version of this problem. In our
case we have a depth restrictions $d(t)\in\mathbb{N}$ for every terminal $t$.
We are looking for a shortest binary rectilinear Steiner arborescence such that
each terminal $t$ is at depth $d(t)$, that is, there are exactly $d(t)$ Steiner
points on the unique root-$t$-path is exactly $d(t)$. We prove that even this
restricted version is NP-hard.
