A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n^2\log n)$ time algorithm to compute the number of pairs of edges that cross in a geometric graph on n vertices. For layered graphs and convex geometric graphs the algorithm takes $O(n^2)$ time.

中文翻译：

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计算几何图形中的交叉数

几何图是这样的图，其顶点是平面中一般位置上的点，并且其边缘是连接这些点的直线段。在本文中，我们给出了$Ø（{ñ}^2\mathrm{日志}ñ）$时间算法来计算在n个顶点上的几何图形中相交的边对的数量。对于分层图和凸几何图，算法需要$Ø（{ñ}^2）$ 时间。