  Based on Welzl's algorithm for smallest circles and spheres we develop a
simple linear time algorithm for finding the smallest circle enclosing a point
cloud on a sphere. The algorithm yields correct results as long as the point
cloud is contained in a hemisphere, but the hemisphere does not have to be
known in advance and the algorithm automatically detects whether the hemisphere
assumption is met.
  For the full-sphere case, that is, if the point cloud is not contained in a
hemisphere, we provide hints on how to adapt existing linearithmic time
algorithms for spherical Voronoi diagrams to find the smallest enclosing
circle.
