  We develop efficient parameterized, with additive error, approximation
algorithms for the (Connected) $r$-Domination problem and the (Connected)
$p$-Center problem for unweighted and undirected graphs. Given a graph $G$, we
show how to construct a (connected) $\big(r + \mathcal{O}(\mu)
\big)$-dominating set $D$ with $|D| \leq |D^*|$ efficiently. Here, $D^*$ is a
minimum (connected) $r$-dominating set of $G$ and $\mu$ is our graph parameter,
which is the tree-breadth or the cluster diameter in a layering partition of
$G$. Additionally, we show that a $+ \mathcal{O}(\mu)$-approximation for the
(Connected) $p$-Center problem on $G$ can be computed in polynomial time. Our
interest in these parameters stems from the fact that in many real-world
networks, including Internet application networks, web networks, collaboration
networks, social networks, biological networks, and others, and in many
structured classes of graphs these parameters are small constants.
