论文标题
在2个规范图上开槽的在线单方面交叉最小化问题
The Slotted Online One-Sided Crossing Minimization Problem on 2-Regular Graphs
论文作者
论文摘要
在图形图的区域中，单方面交叉最小化问题（OSCM）是在两部分图上定义的，两个顶点集彼此平行并平行于平行，所有边缘都被绘制为直线。任务是找到一个节点集的置换，以便最小化所有边缘边缘交叉点的总数（称为交叉点）。通常，一组节点的程度受到恒定k的限制，而问题则缩写为OSCM-K。 在这项工作中，我们研究了此问题的在线变体，其中已经给出了其中一个节点集。另一个节点集和事件边缘迭代显示，每个节点必须插入占位符，我们称之为插槽。目标是再次最大程度地减少最终图中的交叉数量。以在线方式最小化交叉点与动态图形图的更经验领域有关。请注意，开槽的OSCM问题使实例更难求解在线算法，但是在离线情况下，它等同于没有插槽的版本。 我们表明，在线插槽的OSCM-K对于任何k的任何k或等于2均不具有竞争力，随后将图类类限制为2个规范图的竞争力，为此，我们显示了4/3的下限，竞争比率为5。
In the area of graph drawing, the One-Sided Crossing Minimization Problem (OSCM) is defined on a bipartite graph with both vertex sets aligned parallel to each other and all edges being drawn as straight lines. The task is to find a permutation of one of the node sets such that the total number of all edge-edge intersections, called crossings, is minimized. Usually, the degree of the nodes of one set is limited by some constant k, with the problem then abbreviated to OSCM-k. In this work, we study an online variant of this problem, in which one of the node sets is already given. The other node set and the incident edges are revealed iteratively and each node has to be inserted into placeholders, which we call slots. The goal is again to minimize the number of crossings in the final graph. Minimizing crossings in an online way is related to the more empirical field of dynamic graph drawing. Note the slotted OSCM problem makes instances harder to solve for an online algorithm but in the offline case it is equivalent to the version without slots. We show that the online slotted OSCM-k is not competitive for any k greater or equal 2 and subsequently limit the graph class to that of 2-regular graphs, for which we show a lower bound of 4/3 and an upper bound of 5 on the competitive ratio.
