Intersecting ellipses induced by a max-sum matching

Polina Barabanshchikova () and Alexandr Polyanskii ()
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Polina Barabanshchikova: Moscow Institute of Physics and Technology
Alexandr Polyanskii: Bulgarian Academy of Sciences

Journal of Global Optimization, 2024, vol. 88, issue 2, No 5, 395-407

Abstract: 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 $$\sqrt{3} / 2$$ 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.

Keywords: Infinite descent; Convex optimization; Tverberg theorem; Max-sum matching; Alternating cycle; 51K99; 05C50; 51F99; 52C99; 05A99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01312-w

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