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In a multihop wireless network, each node has a transmission radius and is able to send a message to all of its neighbors that are located within the radius. In a broadcasting task, a source node sends the same message to all the nodes in the network. In this paper, we propose to significantly reduce or eliminate the communication overhead of a broadcasting task by applying the concept of localized dominating sets. Their maintenance does not require any communication overhead in addition to maintaining positions of neighboring nodes. Retransmissions by only internal nodes in a dominating set is sufficient for reliable broadcasting. Existing dominating sets are improved by using node degrees instead of their ids as primary keys. We also propose to eliminate neighbors that already received the message and rebroadcast only if the list of neighbors that might need the message is nonempty. A retransmission after …