The classical minimum connected dominating set (MinCDS) problem aims to find
a minimum-size subset of connected nodes in a network such that every other
node has at least one neighbor in the subset. This problem is drawing
considerable attention in the field of wireless sensor networks because
connected dominating sets can serve as virtual backbones of such networks.
Considering fault-tolerance, researchers developed the minimum k-connected
m-fold CDS (Min(k,m)CDS) problem. Many studies have been conducted on
MinCDSs, especially those in unit disk graphs. However, for the minimum-weight
CDS (MinWCDS) problem in general graphs, algorithms with guaranteed
approximation ratios are rare. Guha and Khuller designed a
(1.35+ε)lnn-approximation algorithm for MinWCDS, where n is the
number of nodes. In this paper, we improved the approximation ratio to
2H(δmax+m−1) for MinW(1,m)CDS, where δmax is the
maximum degree of the graph