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We propose several localized algorithms to achieve energy-efficient broadcasting in wireless multihop networks using directional antennas. Each node needs to know only geographic position of itself and its neighbors. Our first protocol is called DRBOP and it follows the one-to-one communication model to reach to all nodes in the relative neighborhood graph (RNG). Each node that receives a message for the first time from one of its RNG neighbors will rebroadcast it to each of its remaining RNG neighbors separately. The transmission power is adjusted for each transmission to the minimal necessary for reaching the particular neighbor. Next, we describe DLBOP, where RNG is replaced by the localized minimum spanning tree (LMST) graph which is a localized topology resembling the minimum spanning tree. We then observe that, for very dense networks, it is more energy-efficient to reach more than one neighbor at a time. A one-to-many protocol efficient for dense networks is proposed. We then describe an efficient localized protocol which adaptively switches (without any threshold) between one-to-one and one-to-many communication models and is efficient for both sparse and dense networks. Our simulation results show that for different energy models, the adaptive protocol is able to achieve a competitive performance to globalized algorithms while having a fully localized operation.