当前位置: X-MOL 学术Comput. Geom. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
1-bend upward planar slope number of SP-digraphs
Computational Geometry ( IF 0.4 ) Pub Date : 2020-02-26 , DOI: 10.1016/j.comgeo.2020.101628
Emilio Di Giacomo , Giuseppe Liotta , Fabrizio Montecchiani

It is proved that every series-parallel digraph whose maximum vertex degree is Δ admits an upward planar drawing with at most one bend per edge such that each edge segment has one of Δ distinct slopes. The construction is worst-case optimal in terms of the number of slopes, and it gives rise to drawings with optimal angular resolution πΔ. A variant of the drawing algorithm is used to show that (non-directed) reduced series-parallel graphs and flat series-parallel graphs have a (non-upward) 1-bend planar drawing with Δ2 distinct slopes if biconnected, and with Δ2+1 distinct slopes if connected.



中文翻译:

SP图的一弯向上平面斜率数

事实证明,每一个最大顶点度为Δ的串并平行图都允许一个向上的平面图,每个边缘最多具有一个弯曲,使得每个边缘段都具有Δ个不同的斜率之一。就坡度的数量而言,此结构在最坏情况下是最佳的,从而产生具有最佳角度分辨率的图形πΔ。绘制算法的一种变体用于显示(无向)精简系列-平行图和平面系列-平行图具有(非向上)1-弯曲平面图,其中Δ2 双向连接时有明显的坡度 Δ2+1个 如果连接,则有明显的斜坡。

更新日期:2020-02-26
down
wechat
bug