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Improved algorithms for the bichromatic two-center problem for pairs of points
Computational Geometry ( IF 0.4 ) Pub Date : 2021-07-09 , DOI: 10.1016/j.comgeo.2021.101806
Haitao Wang 1 , Jie Xue 2
Affiliation  

We consider a bichromatic two-center problem for pairs of points. Given a set S of n pairs of points in the plane, for every pair, we want to assign a red color to one point and a blue color to the other, in such a way that the value max{r1,r2} is minimized, where r1 (resp., r2) is the radius of the smallest enclosing disk of all red (resp., blue) points. Previously, an exact algorithm of O(n3log2n) time and a (1+ε)-approximate algorithm of O(n+(1/ε)6log2(1/ε)) time were known. In this paper, we propose a new exact algorithm of O(n2log2n) time and a new (1+ε)-approximate algorithm of O(n+(1/ε)3log2(1/ε)) time.



中文翻译:

点对双色双中心问题的改进算法

我们考虑点对的双色双中心问题。给定平面中由n对点组成的集合S,对于每一对点,我们希望为一个点分配红色,为另一个点分配蓝色,这样值最大限度{r1,r2} 被最小化,其中 r1 (分别, r2) 是所有红色(或蓝色)点的最小封闭圆盘的半径。以前,一个精确的算法(n3日志2n) 时间和一个 (1+ε)- 近似算法 (n+(1/ε)6日志2(1/ε))时间为人所知。在本文中,我们提出了一种新的精确算法(n2日志2n) 时间和新的 (1+ε)- 近似算法 (n+(1/ε)3日志2(1/ε)) 时间。

更新日期:2021-07-30
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