Broadcasting is an effective means for disseminating information i n wireless ad hoc networks. I n this paper we propose a novel distributed broadcasting protocol in wireless ad hoc networks, which is based on an highly eficient metric for characterizing the importance of a node, with respect to its contribution in covering the local neighborhood. The protocol is reliable and achieves small communication complexity with linear in the number of nodes computation complexity. Experimental results for a large variety of network topologies show that the proposed algorithm is capable of generating small connected dominating sets, which guarantee a relatively small number of rebroadcasts.