  In this paper we consider finding a geometric minimum-sum dipolar spanning
tree in R^3, and present an algorithm that takes O(n^2 log^2 n) time using
O(n^2) space, thus almost matching the best known results for the planar case.
Our solution uses an interesting result related to the complexity of the common
intersection of n balls in R^3, of possible different radii, that are all
tangent to a given point p. The problem has applications in communication
networks, when the goal is to minimize the distance between two hubs or servers
as well as the distance from any node in the network to the closer of the two
hubs. The approach used in this paper also provides a solution to the discrete
2-center problem in R^3 within the same time and space bounds.
