AI 中文总结
研究如何将图可视化为特定图形并使边交叉数最少，虽该问题对一般弧图NP难，但可利用分层图宽度这一参数，通过固定参数可处理的线性时间算法，借助广度优先搜索获得分层图来解决。
AI 中文摘要
我们展示了如何将图\(G=(V,E)\)可视化为具有最少边交叉数的分层图、尊重层的弧图或尊重层的线性柱面图，其中尊重层意味着层按顺序出现在一条直线上且顶点按层分组。尽管对于一般弧图此问题是NP难的，但我们展示了如何用固定参数可处理的线性时间算法创建此类图，允许这样做的参数是分层图的宽度。分层图可通过广度优先搜索（BFS）获得，此时宽度由称为BFS宽度的图宽度参数上界界定。
英文摘要
We show how to visualize a graph, $G=(V,E)$, as a layered drawing, layer-respecting arc diagram, or layer-respecting linear cylindric drawing with a minimum number of edge crossings, where layer-respecting means that layers appear in order on a single line and vertices are grouped by their layers. Even though this problem is NP-hard for general arc diagrams, we show how to create such diagrams with fixed-parameter tractable linear-time algorithms, where the parameter that allows this is the width of a layered graph. Such a layered graph can be obtained from a breadth-first search (BFS), in which case the width is upper bounded by a graph width parameter called the BFS width.
CommentsFull version of the paper published at CCCG 2026
