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Multipoint relays (MPR) provide a localized and optimized way of broadcasting messages in a mobile ad hoc network (MANET). Using partial 2-hop information, each node chooses a small set of forward neighbors to relay messages and this set covers the node's 2-hop neighbor set. These selected forward nodes form a connected dominating set (CDS) to ensure full coverage. Adjih et al. later proposed a novel extension of MPR to construct a small CDS and it is source-independent. In this paper, we provide several extensions to generate a smaller CDS using complete 2-hop information to cover each node's 2-hop neighbor set. We extend the notion of coverage in the original MPR. We prove that the extended MPR has a constant local approximation ratio compared with a logarithmic local ratio in the original MPR. In addition, we show that the extended MPR has a constant global probabilistic approximation ratio, while no such ratio exists in the original MPR and its existing extensions. The effectiveness of our approach is confirmed through a simulation study.