  A subset $S$ of nodes in a graph $G$ is a $k$-connected $m$-dominating set
($(k,m)$-cds) if the subgraph $G[S]$ induced by $S$ is $k$-connected and every
$v \in V \setminus S$ has at least $m$ neighbors in $S$. In the $k$-Connected
$m$-Dominating Set ($(k,m)$-CDS) problem the goal is to find a minimum weight
$(k,m)$-cds in a node-weighted graph. For $m \geq k$ we obtain the following
approximation ratios. For general graphs our ratio $O(k \ln n)$ improves the
previous best ratio $O(k^2 \ln n)$ and matches the best known ratio for unit
weights. For unit disc graphs we improve the ratio $O(k \ln k)$ to
$\min\left\{\frac{m}{m-k},k^{2/3}\right\} \cdot O(\ln^2 k)$ -- this is the
first sublinear ratio for the problem, and the first polylogarithmic ratio
$O(\ln^2 k)/\epsilon$ when $m \geq (1+\epsilon)k$; furthermore, we obtain ratio
$\min\left\{\frac{m}{m-k},\sqrt{k}\right\} \cdot O(\ln^2 k)$ for uniform
weights. These results are obtained by showing the same ratios for the Subset
$k$-Connectivity problem when the set $T$ of terminals is an $m$-dominating set
with $m \geq k$.
