论文标题
由最大和匹配引起的相交椭圆形
Intersecting ellipses induced by a max-sum matching
论文作者
论文摘要
对于平面中的一组点，请选择一个最大匹配，即最大程度地匹配其边缘的欧几里得距离之和。对于最大和匹配的每个边缘，请考虑在边缘的端点和偏心$ \ sqrt 3 /2 $处使用foci的椭圆。使用优化方法，我们证明了由这些椭圆界定的凸组集合，从1995年开始回答了安迪·芬格特（Andy Fingerhut）的特维尔伯格型问题。
For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum matching, consider the ellipse with foci at the edge's endpoints and eccentricity $\sqrt 3 / 2$. Using an optimization approach, we prove that the convex sets bounded by these ellipses intersect, answering a Tverberg-type question of Andy Fingerhut from 1995.
