  We obtain algorithms for computing Tverberg partitions based on centerpoint
approximations. This applies to a wide range of convexity spaces, from the
classic Euclidean setting to geodetic convexity in graphs. In the Euclidean
setting, we present probabilistic algorithms which are weakly polynomial in the
number of points and the dimension. For geodetic convexity in graphs, we obtain
deterministic algorithms for cactus graphs and show that the general problem of
finding the Radon number is NP-hard.
