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arXiv · 1409.8055

The 2-center problem and ball operators in strictly convex normed planes

Pedro Martín·Horst Martini·Margarita Spirova
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Abstract

We investigate the 2-center problem for arbitrary strictly convex, centrally symmetric curves instead of usual circles. In other words, we extend the 2-center problem (from the Euclidean plane) to strictly convex normed planes, since any strictly convex, centrally symmetric curve can be interpreted as (unit) circle of such a normed plane. Thus we generalize the respective algorithmical approach given by J. Hershberger for the Euclidean plane. We show that the corresponding decision problem can be solved in $O(n^2\log\, n)$ time. In addition, we prove various theorems on the notions of ball hull and ball intersection of finite sets in strictly convex normed planes, which are fundamental for the 2-center problem, but also interesting for themselves.

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Pedro Martín, Horst Martini, Margarita Spirova. 2014-09-29. The 2-center problem and ball operators in strictly convex normed planes. https://arxiv.org/abs/1409.8055

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