Circles through two points that always enclose many points

Circles through two points that always enclose many points
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通过总是包含许多点的两个点的圆

DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
X. Shen
X. Shen
中科院分区：
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文献类型：
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作者：
H. Edelsbrunner;N. Hasan;R. Seidel;X. Shen

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摘要本文证明了平面上任意n个点的集合包含两个点，使得任何经过这两个点的圆至少包围这两个点
AbstractThis paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least $$nleft( {1/2 - 1sqrt {12} } ight) + O(1) approx n/4 cdot 7$$ points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.