  We consider clustering in the perturbation resilience model that has been
studied since the work of Bilu and Linial [ICS, 2010] and Awasthi, Blum and
Sheffet [Inf. Proc. Lett., 2012]. A clustering instance $I$ is said to be
$\alpha$-perturbation resilient if the optimal solution does not change when
the pairwise distances are modified by a factor of $\alpha$ and the perturbed
distances satisfy the metric property --- this is the metric perturbation
resilience property introduced in Angelidakis et. al. [STOC, 2010] and a weaker
requirement than prior models. We make two high-level contributions.
  1) We show that the natural LP relaxation of $k$-center and asymmetric
$k$-center is integral for $2$-perturbation resilient instances. We belive that
demonstrating the goodness of standard LP relaxations complements existing
results that are based on combinatorial algorithms designed for the
perturbation model.
  2) We define a simple new model of perturbation resilience for clustering
with \emph{outliers}. Using this model we show that the unified MST and dynamic
programming based algorithm proposed by Angelidakis et. al. [STOC, 2010]
exactly solves the clustering with outliers problem for several common center
based objectives (like $k$-center, $k$-means, $k$-median) when the instances is
$2$-perturbation resilient. We further show that a natural LP relxation is
integral for $2$-perturbation resilient instances of \kcenter with outliers.
