Before revision:  Our result can be viewed as a new step along the direction of beyond worst-case analysis. We also show that our ideas can be extended to be more general techniques, a novel uniform-adaptive sampling method and a sandwich lemma, for solving the general case of MEB with outliers ( i.e., without the stability assumption) and the problem of k-center clustering with outliers.
After revision:   i.e., without the stability assumption) and the problem of k-center clustering with outliers.