有两个斜面的向上平面图
Upward planar drawings with two slopes
摘要：
在有向图的向上平面2-斜率绘图中，仅使用两个不同的斜率将边绘制为向上方向上的直线段而不交叉。我们研究了一个给定的向上平面有向图是否允许这样的绘图，如果允许的话，如何构造它.对于固定嵌入的情况下，我们给出了一个简单的特征和线性时间的结构，采用算法从正交绘图.对于变量嵌入的情况下，我们描述了一个线性时间算法的单源有向图，串并行有向图的四分之一时间算法，和一个固定参数的一般有向图的易处理的算法。对于后两个类，我们利用SPQR树和向上螺旋的概念。作为这种绘画风格的一个应用，我们展示了如何绘制一个向上的平面系统发育网络，两个斜坡，使所有的叶子都位于一条水平线上。
英文摘要：
In an upward planar 2-slope drawing of a digraph, edges are drawn as straight-line segments in the upward direction without crossings using only two different slopes. We investigate whether a given upward planar digraph admits such a drawing and, if so, how to construct it. For the fixed embedding scenario, we give a simple characterisation and a linear-time construction by adopting algorithms from orthogonal drawings. For the variable embedding scenario, we describe a linear-time algorithm for single-source digraphs, a quartic-time algorithm for series-parallel digraphs, and a fixed-parameter tractable algorithm for general digraphs. For the latter two classes, we make use of SPQR-trees and the notion of upward spirality. As an application of this drawing style, we show how to draw an upward planar phylogenetic network with two slopes such that all leaves lie on a horizontal line.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
