Bottleneck bichromatic full steiner trees

Given two sets of points in the plane, Q of n (terminal) points and S of m (Steiner) points, where each of Q and S contains bichromatic points (red and blue points), a full bichromatic Steiner tree is a Steiner tree in which all points of Q are leaves and each edge of the tree is bichromatic (i.e., connects a red and a blue point). In the bottleneck bichromatic full Steiner tree (BBFST) problem, the goal is to compute a bichromatic full Steiner tree T, such that the length of the longest edge in T is minimized. In k-BBFST problem, the goal is to find a bichromatic full Steiner tree T with at most k ≤ m Steiner points from S, such that the length of the longest edge in T is minimized. In this paper, we present an O((n + m) log m) time algorithm that solves the BBFST problem. Moreover, we show that k-BBFST problem is NP-hard and we give a polynomial-time 9-approximation algorithm for the problem.