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 is an m-fold connected dominating set (m-fold CDS) of graph if every node in has at least neighbors in and the subgraph of induced by is connected. In this paper, we will present a greedy algorithm to compute an -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 (.) is the Harmonic number.