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Recent research points out that the flooding mechanism for topology update or route request in existing ad hoc routing protocols greatly degrades the network capacity. If we restrict the broadcast of control packets within a small subset of hosts in the network, the protocol overhead can be substantially reduced. This motivates our research of constructing a virtual backbone by computing a connected dominating set (CDS) in unit‐disk graphs. In this paper, we propose two distributed algorithms to approximate a minimum CDS. These algorithms take linear time. Their performance is verified by a complete theoretical analysis. Copyright © 2006 John Wiley & Sons, Ltd.