# A greedy algorithm for the fault-tolerant connected dominating set in a general graph

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## Abstract

Using a connected dominating set (CDS) to serve as the virtual backbone of a wireless network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to an accidental damage or energy depletion, it is desirable that the virtual backbone is fault tolerant. A node set \(C\) is an \(m\)-fold connected dominating set (\(m\)-fold CDS) of graph \(G\) if every node in \(V(G)\setminus C\) has at least \(m\) neighbors in \(C\) and the subgraph of \(G\) induced by \(C\) is connected. In this paper, we will present a greedy algorithm to compute an \(m\)-fold CDS in a general graph, which has size at most \(2+\ln (\Delta +m-2)\) times that of a minimum \(m\)-fold CDS, where \(\Delta \) is the maximum degree of the graph. This result improves on the previous best known performance ratio of \(2H(\Delta +m-1)\) for this problem, where \(H(\cdot )\) is the Harmonic number.

## Keywords

\(m\)-fold connected dominating set Non-submodular potential function Greedy algorithm## Notes

### Acknowledgments

This research is supported by NSFC (61222201) and SRFDP (20126501110001), and by National Science Foundation of USA under grants CNS0831579 and CCF0728851.

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