  Let P be a set of n points in R^3. The 2-center problem for P is to find two
congruent balls of minimum radius whose union covers P. We present two
randomized algorithms for computing a 2-center of P. The first algorithm runs
in O(n^3 log^5 n) expected time, and the second algorithm runs in O((n^2 log^5
n) /(1-r*/r_0)^3) expected time, where r* is the radius of the 2-center balls
of P and r_0 is the radius of the smallest enclosing ball of P. The second
algorithm is faster than the first one as long as r* is not too close to r_0,
which is equivalent to the condition that the centers of the two covering balls
be not too close to each other.
