We study the upward point-set embeddability of digraphs on one-sided convex point sets with at most 1 bend per edge. We provide an algorithm to compute a 1-bend upward point-set embedding of outerplanar $st$-digraphs on arbitrary one-sided convex point sets. We complement this result by proving that for every $n \geq 18$ there exists a $2$-outerplanar $st$-digraph $G$ with $n$ vertices and a one-sided convex point set $S$ so that $G$ does not admit a 1-bend upward point-set embedding on $S$.

翻译：我们研究有向图在单侧凸点集上、每条边最多允许一个拐点的上向点集可嵌入性。针对外平面$st$-有向图，我们提出了一种在任意单侧凸点集上计算其单拐点上向点集嵌入的算法。作为补充，我们证明对于任意$n \geq 18$，存在一个包含$n$个顶点的$2$-外平面$st$-有向图$G$及一个单侧凸点集$S$，使得$G$在$S$上不存在单拐点上向点集嵌入。