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Using a connected dominating set (CDS) to serve as the virtual backbone of awireless sensor network (WSN) is an effective way to save energy and reduce theimpact of broadcasting storms. Since nodes may fail due to accidental damage orenergy depletion, it is desirable that the virtual backbone is fault tolerant.This could be modeled as a k-connected, m-fold dominating set ((k,m)-CDS).Given a virtual undirected network G=(V,E), a subset C\subset V is a (k,m)-CDSof G if (i) G[C], the subgraph of G induced by C is k-connected, and (ii) eachnode in V\C has at least m neighbors in C. We present a two-phase greedyalgorithm for computing a (2,2)-CDS that achieves an asymptotic approximationfactor of $(3+\ln(\Delta+2))$, where $\Delta$ is the maximum degree of G. Thisresult improves on the previous best known performance factor of$(4+\ln\Delta+2\ln(2+\ln\Delta))$ for this problem.

A greedy approximation algorithm for the minimum (2,2)-connected dominating set problem