We investigate the problem of drawing two posets of the same ground set so that one is drawn from left to right and the other one is drawn from the bottom up. The input to this problem is a directed graph $G = (V, E)$ and two sets $X, Y$ with $X \cup Y = E$, each of which can be interpreted as a partial order of $V$. The task is to find a planar drawing of $G$ such that each directed edge in $X$ is drawn as an $x$-monotone edge, and each directed edge in $Y$ is drawn as a $y$-monotone edge. Such a drawing is called an $xy$-planar drawing. Testing whether a graph admits an $xy$-planar drawing is NP-complete in general. We consider the case that the planar embedding of $G$ is fixed and the subgraph of $G$ induced by the edges in $Y$ is a connected spanning subgraph of $G$ whose upward embedding is fixed. For this case we present a linear-time algorithm that determines whether $G$ admits an $xy$-planar drawing and, if so, produces an $xy$-planar polyline drawing with at most three bends per edge.

中文翻译：

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绘制两个姿势

我们研究了绘制相同地面集的两个偏序集的问题，其中一个从左到右绘制，另一个从下向上绘制。这个问题的输入是一个有向图 $G = (V, E)$ 和两个集合 $X, Y$ 和 $X \cup Y = E$，每一个都可以解释为 $V$ 的偏序. 任务是找到 $G$ 的平面图，使得 $X$ 中的每条有向边绘制为 $x$-单调边，$Y$ 中的每条有向边绘制为 $y$-单调边. 这种绘图称为$xy$-平面绘图。测试图形是否承认 $xy$-平面图通常是 NP 完全的。我们考虑$G$的平面嵌入是固定的，$Y$中的边诱导的$G$子图是$G$的连通生成子图，其向上嵌入是固定的。