近似捆绑交叉数
Approximating the Bundled Crossing Number
摘要：
交叉点捆绑是一种提高图形可读性的策略。在本文中，我们认为好的图纸，即，我们要求任何两条边最多有一个公共点，该公共点可以是公共顶点或交叉点。我们的主要结果是，有一个多项式时间的算法来计算一个好的绘图（添加一个术语取决于面部结构的绘图）的捆绑交叉数的8-近似。在圆形图的特殊情况下，近似因子为8（没有额外的项），这改进了Fink等人的10-近似（嵌入图中的捆绑交叉，Proc. Latin'16）。我们的方法也适用于伪片段族的相同近似因子，即，最多相交一次的曲线。我们还展示了如何计算一个9/2近似时的交叉图的伪段是二分的。
英文摘要：
Bundling crossings is a strategy which can enhance the readability of drawings. In this paper we consider good drawings, i.e., we require that any two edges have at most one common point which can be a common vertex or a crossing. Our main result is that there is a polynomial time algorithm to compute an 8-approximation of the bundled crossing number of a good drawing (up to adding a term depending on the facial structure of the drawing). In the special case of circular drawings the approximation factor is 8 (no extra term), this improves upon the 10-approximation of Fink et al. (Bundled crossings in embedded graphs, Proc. Latin'16). Our approach also works with the same approximation factor for families of pseudosegments, i.e., curves intersecting at most once. We also show how to compute a 9/2-approximation when the intersection graph of the pseudosegments is bipartite.
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。
