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In this paper, we present a polynomial dynamic programming algorithm thattests whether a $n$-vertex directed tree $T$ has an upward planar embeddinginto a convex point-set $S$ of size $n$. Further, we extend our approach to theclass of outerplanar digraphs. This nontrivial and surprising result impliesthat any given digraph can be efficiently tested for an upward planar embeddinginto a given convex point set.

Upward Point Set Embeddability for Convex Point Sets is in $P$