The Very Best of Perfect Non-crossing Matchings.

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.