  Given a dataset $V$ of points from some metric space, the popular $k$-center
problem requires to identify a subset of $k$ points (centers) in $V$ minimizing
the maximum distance of any point of $V$ from its closest center. The
\emph{robust} formulation of the problem features a further parameter $z$ and
allows up to $z$ points of $V$ (outliers) to be disregarded when computing the
maximum distance from the centers. In this paper, we focus on two important
constrained variants of the robust $k$-center problem, namely, the Robust
Matroid Center (RMC) problem, where the set of returned centers are constrained
to be an independent set of a matroid of rank $k$ built on $V$, and the Robust
Knapsack Center (RKC) problem, where each element $i\in V$ is given a positive
weight $w_i<1$ and the aggregate weight of the returned centers must be at most
1. We devise coreset-based strategies for the two problems which yield
efficient sequential, MapReduce, and Streaming algorithms. More specifically,
for any fixed $\epsilon>0$, the algorithms return solutions featuring a
$(3+\epsilon)$-approximation ratio, which is a mere additive term $\epsilon$
away from the 3-approximations achievable by the best known polynomial-time
sequential algorithms for the two problems. Moreover, the algorithms
obliviously adapt to the intrinsic complexity of the dataset, captured by its
doubling dimension $D$. For wide ranges of the parameters $k,z,\epsilon, D$, we
obtain a sequential algorithm with running time linear in $|V|$, and
MapReduce/Streaming algorithms with few rounds/passes and substantially
sublinear local/working memory.
