— As broadcasting is widely used for miscellaneous maintenance operations in wireless ad hoc networks, where energy is a scarce resource, an efficient broadcasting protocol is of prime importance. One of the best known algorithm, named BIP (Broadcast Incremental Power), constructs a spanning tree rooted at a given node. This protocol offers very good results in terms of energy savings, but its computation is unfortunately centralized, as the source node needs to know the entire topology of the network to compute the tree. Many localized protocols have since been proposed, but none of them has ever reached the performances of BIP. Even distributed versions of the latter have been proposed, but they require a huge transmission overhead for information exchange and thus waste energy savings obtained thanks to the efficiency of the tree. In this paper, we propose and analyze a localized version of this protocol. In our method, each node is aware of the position of all the hosts in the ...