We study the planar orthogonal drawing style within the framework of partial representation extension. Let $(G,H,{\Gamma}_H )$ be a partial orthogonal drawing, i.e., G is a graph, $H\subseteq G$ is a subgraph and ${\Gamma}_H$ is a planar orthogonal drawing of H. We show that the existence of an orthogonal drawing ${\Gamma}_G$ of $G$ that extends ${\Gamma}_H$ can be tested in linear time. If such a drawing exists, then there also is one that uses $O(|V(H)|)$ bends per edge. On the other hand, we show that it is NP-complete to find an extension that minimizes the number of bends or has a fixed number of bends per edge.

中文翻译：

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扩展部分正交图形

我们研究了局部表示扩展框架内的平面正交绘图风格。设 $(G,H,{\Gamma}_H )$ 是部分正交图，即 G 是图，$H\subseteq G$ 是子图，${\Gamma}_H$ 是平面正交图H. 我们表明，扩展 ${\Gamma}_H$ 的 $G$ 的正交绘图 ${\Gamma}_G$ 的存在可以在线性时间内进行测试。如果存在这样的图纸，那么还有一个使用 $O(|V(H)|)$ 每条边弯曲。另一方面，我们表明，找到最小化弯曲数量或每条边具有固定弯曲数量的扩展是 NP 完全的。