  In this paper, we study the problem of {\em $k$-center clustering with
outliers}. The problem has many important applications in real world, but the
presence of outliers can significantly increase the computational complexity.
Though a number of methods have been developed in the past decades, it is still
quite challenging to design quality guaranteed algorithm with low complexity
for this problem. Our idea is inspired by the greedy method, Gonzalez's
algorithm, that was developed for solving the ordinary $k$-center clustering
problem. Based on some novel observations, we show that a simple randomized
version of this greedy strategy actually can handle outliers efficiently. We
further show that this randomized greedy approach also yields small coreset for
the problem in doubling metrics (even if the doubling dimension is not given),
which can greatly reduce the computational complexity. Moreover, together with
the partial clustering framework proposed in arXiv:1703.01539 , we prove that
our coreset method can be applied to distributed data with a low communication
complexity. The experimental results suggest that our algorithms can achieve
near optimal solutions and yield lower complexities comparing with the existing
methods.
