We present algorithms that extend the path-based hierarchical drawing framework and give experimental results. Our algorithms run in $O(km)$ time, where $k$ is the number of paths and $m$ is the number of edges of the graph, and provide better upper bounds than the original path based framework: e.g., the height of the resulting drawings is equal to the length of the longest path of $G$, instead of $n-1$, where $n$ is the number of nodes. Additionally, we extend this framework, by bundling and drawing all the edges of the DAG in $O(m + n \log n)$ time, using minimum extra width per path. We also provide some comparison to a well known hierarchical drawing framework, widely known as the Sugiyama framework, as a proof of concept. The experimental results show that our algorithms produce drawings that are better in area and number of bends, but worse for crossings in sparse graphs. Hence, our technique offers an interesting alternative for drawing hierarchical graphs. Finally, we present an $O(m + k \log k)$ time algorithm that computes a specific order of the paths in order to reduce the total edge length and number of crossings and bends.

中文翻译：

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比较两个层次绘图框架的算法和实验

我们提出了扩展基于路径的分层绘图框架并给出实验结果的算法。我们的算法以$ O（km）$的时间运行，其中$ k $是路径数，$ m $是图形的边数，并且比基于原始路径的框架提供更好的上限：例如，高度得到的图形中的等于最长路径$ G $的长度，而不是$ n-1 $，其中$ n $是节点数。此外，我们通过在$ O（m + n \ log n）$时间内捆绑和绘制DAG的所有边缘，并使用每条路径的最小额外宽度来扩展此框架。我们还提供了与众所周知的分层绘图框架（称为Sugiyama框架）的一些比较，以证明概念。实验结果表明，我们的算法所产生的图形在弯曲的面积和数量上都更好，但对于稀疏图中的交叉点更糟。因此，我们的技术为绘制层次图提供了一种有趣的替代方法。最后，我们提出一种$ O（m + k \ log k）$时间算法，该算法计算路径的特定顺序，以减少总边缘长度以及交叉和折弯的数量。