  In this paper, we consider the $k$-center/median/means clustering with
outliers problems (or the $(k, z)$-center/median/means problems) in the
distributed setting. Most previous distributed algorithms have their
communication costs linearly depending on $z$, the number of outliers. Recently
Guha et al. overcame this dependence issue by considering bi-criteria
approximation algorithms that output solutions with $2z$ outliers. For the case
where $z$ is large, the extra $z$ outliers discarded by the algorithms might be
too large, considering that the data gathering process might be costly. In this
paper, we improve the number of outliers to the best possible $(1+\epsilon)z$,
while maintaining the $O(1)$-approximation ratio and independence of
communication cost on $z$. The problems we consider include the $(k, z)$-center
problem, and $(k, z)$-median/means problems in Euclidean metrics.
Implementation of the our algorithm for $(k, z)$-center shows that it
outperforms many previous algorithms, both in terms of the communication cost
and quality of the output solution.
