Before revision:  We achieve sub-linear time bi-criteria approximation algorithms for these problems respectively; the algorithms have sample sizes independent of the number of points n and the dimensionality d, which significantly improve the time complexities of existing algorithms .
After revision:  We achieve sub-linear time bi-criteria approximations, where the "bi-criteria" means that the solution has to allow the approximations on the radius and the number of covered points. Differently, all the algorithms proposed in this paper yield single-criterion approximations (with respect to radius) .