Given a set of points in the plane, we are interested in matching them with straight line segments. We focus on perfect (all points are matched) non-crossing (no two edges intersect) matchings. Apart from the well known MinMax variation, where the length of the longest edge is minimized, we extend work by looking into different optimization variants such as MaxMin, MinMin, and MaxMax. We consider both the monochromatic and bichromatic versions of these problems and provide efficient algorithms for various input point configurations.

中文翻译：

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最好的完美非交叉匹配

给定平面中的一组点，我们有兴趣将它们与直线段进行匹配。我们专注于完美（所有点都匹配）非交叉（没有两条边相交）匹配。除了众所周知的 MinMax 变体（其中最长边的长度被最小化）之外，我们还通过研究不同的优化变体（例如 MaxMin、MinMin 和 MaxMax）来扩展工作。我们考虑了这些问题的单色和双色版本，并为各种输入点配置提供了有效的算法。