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arXiv · 2212.14200

Intersecting ellipses induced by a max-sum matching

Polina Barabanshchikova·Alexandr Polyanskii
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Abstract

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.

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Polina Barabanshchikova, Alexandr Polyanskii. 2022-12-29. Intersecting ellipses induced by a max-sum matching. https://doi.org/10.1007/s10898-023-01312-w

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