Improved Coresets and Sublinear Algorithms for Power Means in Euclidean Spaces Vincent Cohen-Addad Google Research, Zurich. David Saulpic Sorbonne Universit e, Paris Chris Schwiegelshohn

Special cases of problem include the well-known Fermat-Weber problem - or geometric median problem - where z = 1, the mean or centroid where z = 2, and the Minimum Enclosing Ball problem, where z = . We consider these problem in the big data regime. Here, we are interested in sampling as few points as possible such that we can accurately estimate m. More specifically, we consider sublinear algorithms as well as coresets for these problems. Sublinear algorithms have a random query access to the set A and the goal is to minimize the number of queries.