1 research outputs found
Approximation Algorithm for Minimum Weight Connected -Fold Dominating Set
Using connected dominating set (CDS) to serve as a virtual backbone in a
wireless networks can save energy and reduce interference. Since nodes may fail
due to accidental damage or energy depletion, it is desirable that the virtual
backbone has some fault-tolerance. A -connected -fold dominating set
(-CDS) of a graph is a node set such that every node in
has at least neighbors in and the subgraph of
induced by is -connected. Using -CDS can tolerate the failure of
nodes. In this paper, we study Minimum Weight -CDS
problem (-MWCDS), and present an
-approximation algorithm, where is the
maximum degree of the graph and is the Harmonic number. Notice that
there is a -approximation algorithm for the -MWCDS problem,
where is the number of nodes in the graph. Though our constant in is larger than 1.35, is replaced by . Such a replacement
enables us to obtain a -approximation for the -MWCDS
problem on unit disk graphs