A greedy algorithm for the fault-tolerant connected dominating set in a general graph
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
- Du DZ, Graham RL, Pardalos PM, Wan PJ, Wu WL, Zhao W. (2008) Analysis of greedy approximation with nonsubmodular potential functions. In: Proceedings 19th ACMSIAM symposium on discrete algorithms, pp 167–175Google Scholar
- Li M, Wan P, Yao F (2009) Tighter approximation bounds for minimum CDS in wireless ad hoc networks. ISAAC’2009 LNCS 5878:699–709Google Scholar
- Wan P, Wang L, Yao F. (2008) Two-phased approximation algorithms for minimum CDS in wireless ad hoc networks. In: IEEE ICDCS, pp 337–344Google Scholar
- Wang W, Kim D, An M, Gao W, Li X, Zhang Z, Wu W (2012) On construction of quality fault-tolerant virtual backbone in wireless networks. IEEE/ACM Trans Netw. doi:10.1109/TNET.2012.2227791
- Wu Y, Wang F, Thai M, Li Y (2007) Constructing \(k\)-connected \(m\)-dominating sets in wireless sensor networks. In: Military communications conference, pp 1–7Google Scholar