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 $\max \{r_1,r_2\}$ is minimized, where $r_1$ (resp., $r_2$) is the radius of the smallest enclosing disk of all red (resp., blue) points. Previously, an exact algorithm of $O(n^3{\log }^{2}n)$ time and a $(1+\epsilon )$-approximate algorithm of $O(n+{(1/\epsilon )}^6{\log }^2(1/\epsilon ))$ time were known. In this paper, we propose a new exact algorithm of $O(n^2{\log }^{2}n)$ time and a new $(1+\epsilon )$-approximate algorithm of $O(n+{(1/\epsilon )}^3{\log }^2(1/\epsilon ))$ time.

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$\mathrm{最大限度}\{r_1,r_2\}$ 被最小化，其中 $r_1$ （分别， $r_2$) 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$哦(n^3{\mathrm{日志}}^{2}n)$ 时间和一个 $(1+\epsilon )$- 近似算法 $哦(n+{(1/\epsilon )}^6{\mathrm{日志}}^2(1/\epsilon ))$时间为人所知。在本文中，我们提出了一种新的精确算法$哦(n^2{\mathrm{日志}}^{2}n)$ 时间和新的 $(1+\epsilon )$- 近似算法 $哦(n+{(1/\epsilon )}^3{\mathrm{日志}}^2(1/\epsilon ))$ 时间。