  Consider a graph with nonnegative node weight. A vertex subset is called a
CDS (connected dominating set) if every other node has at least one neighbor in
the subset and the subset induces a connected subgraph. Furthermore, if every
other node has at least $m$ neighbors in the subset, then the node subset is
called a $(1,m)$CDS. The minimum-weight $(1,m)$CDS problem aims at finding a
$(1,m)$CDS with minimum total node weight. In this paper, we present a new
polynomial-time approximation algorithm for this problem with approximation
ratio $2H(\delta_{\max}+m-1)$, where $\delta_{\max}$ is the maximum degree of
the given graph and $H(\cdot)$ is the Harmonic function, i.e.,
$H(k)=\sum_{i=1}^k \frac{1}{i}$.
