Improved algorithms for the bichromatic two-center problem for pairs of points

We consider a bichromatic two-center problem for pairs of points. Given set S n points in the plane, every pair, we want to assign red color one point and blue other, such way that value max⁡{r1,r2} is minimized, where r1 (resp., r2) radius smallest enclosing disk all blue) Previously, an exact algorithm O(n3log2⁡n) time (1+ε)-approximate O(n+(1/ε)6log2⁡(1/ε)) were known. In this paper, propose new O(n2log2⁡n) O(n+(1/ε)3log2⁡(1/ε)) time.