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Many protocols used in mobile ad hoc networks rely on the broadcasting capability, especially when performing a route discovery process. However, an efficient broadcasting protocol should be devised to reduce the unnecessary redundant rebroadcasting at some nodes (redundancy) as well as to increase the coverage area as much as possible (reachability). A few approaches have been developed in the literature. We propose a bounding algorithm, which is known to be an efficient candidate to accommodate the two goals, that is to increase reachability while limiting redundancy.