Drawing planar graphs using the lmc-ordering
Drawing planar graphs using the lmc-ordering
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使用 lmc 排序绘制平面图
DOI：
10.1109/sfcs.1992.267814
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
G. Kant
中科院分区：
文献类型：
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作者：
G. Kant
作者介绍了一种优化所需区域，最小角度和网格平面图的弯曲数量的方法。主要工具是在三连接平面图的顶点和面上的一种新型订购类型。使用此方法，线性时间和空间算法可以针对许多图形绘图问题设计。他表明，可以用（2n-4）*（n-2）网格上的直线绘制每个三连电的平面图G。如果g具有最高度为四（三）在n*n网格上（（（/sup n /// sub 2/）*（分别为/sup n /// sub 2/）网格）。如果g具有最高度D，则可以在（2n-6）*（3n-6）网格上绘制G平面，最小角度大于/sup 1 /// sub d-2/readians，最多在5n-15弯曲。在某些情况下，这些结果比以前的结果有了很大的改善，在其他情况下给出了新的界限。其他几个结果，例如包括可见性表示。<< etx >>
The author introduces a method to optimize the required area, minimum angle and number of bends of planar drawings of graphs on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. With this method linear time and space algorithms can be designed for many graph drawing problems. He shows that every triconnected planar graph G can be drawn convexly with straight lines on an (2n-4)*(n-2) grid. If G has maximum degree four (three), then G can be drawn orthogonal with at most (/sup 3n///sub 2/)+3 (at most (/sup n///sub 2/)+1) bends on an n*n grid ((/sup n///sub 2/)*(/sup n///sub 2/) grid, respectively). If G has maximum degree d, then G can be drawn planar on an (2n-6)*(3n-6) grid with minimum angle larger than /sup 1///sub d-2/ radians and at most 5n-15 bends. These results give in some cases considerable improvements over previous results, and give new bounds in other cases. Several other results, e.g. concerning visibility representations, are included.<<ETX>>