  We study the problem of Upward Point-Set Embeddability, that is the problem
of deciding whether a given upward planar digraph $D$ has an upward planar
embedding into a point set $S$. We show that any switch tree admits an upward
planar straight-line embedding into any convex point set. For the class of
$k$-switch trees, that is a generalization of switch trees (according to this
definition a switch tree is a $1$-switch tree), we show that not every
$k$-switch tree admits an upward planar straight-line embedding into any convex
point set, for any $k \geq 2$. Finally we show that the problem of Upward
Point-Set Embeddability is NP-complete.
