Planar bichromatic bottleneck spanning trees

Given a set P of red and blue points in the plane, a planar bichrornatic spanning tree of P is a geometric spanning tree of P, such that each edge connects a red and a blue point, and no two edges intersect. In the bottleneck planar bichromatic spanning tree problem, the goal is to find a planar bichromatic spanning tree T, such that the length of the longest edge (i.e., bottleneck) in T is minimized. In this paper, we show that this problem is NP-hard for points in general position. Our main contribution is a polynomial-time (8 root 2)-approximation algorithm, by showing that any bichromatic spanning tree of bottleneck lambda can be converted to a planar bichromatic spanning tree of bottleneck at most 8 root 2 lambda.