A plane graph is rectilinear planar if it admits an embedding-preserving straight-line drawing where each edge is either horizontal or vertical. We prove that rectilinear planarity testing can be solved in optimal $O(n)$ time for any plane series-parallel graph $G$ with $n$ vertices. If $G$ is rectilinear planar, an embedding-preserving rectilinear planar drawing of $G$ can be constructed in $O(n)$ time. Our result is based on a characterization of rectilinear planar series-parallel graphs in terms of intervals of orthogonal spirality that their components can have, and it leads to an algorithm that can be easily implemented.
翻译:平面图是矩形平面图,如果它承认每个边缘为水平或垂直的嵌入- 保存直线绘图。 我们证明,对任何平面序列- 平行图的正直线计划性测试,只要在最佳时间以美元(n) 美元解决,任何平面序列- 平行图$G$,只要以美元为顶点。 如果$G$是直线平面平面图,则可以用美元(n) 时间构建嵌入- 保存直线图$G$的嵌入- 嵌入- 保留直线图。 我们的结果基于对直线- 平线序列- 单列图的定性, 其组成部分可以具有的垂直螺旋周期, 并导致一种易于执行的算法。