The common belief is that localized broadcast algorithms are not able to guarantee both full delivery and a good bound on the number of transmissions. In this paper, we propose the first localized broadcast algorithm that guarantees full delivery and a constant approximation ratio to the minimum number of required transmissions in the worst case. The proposed broadcast algorithm is a self-pruning algorithm based on 1-hop neighbor information. Using the proposed algorithm, each node determines its status (forwarding/non-forwarding) in O(d log(d)), where d is the maximum node degree of the network. By extending the proposed algorithm, we show that localized broadcast algorithms can achieve both full delivery and a constant approximation ratio to the optimum solution with message complexity O(N), where N is the total number of nodes in the network and each message contains a constant number of bits. We also show how to save bandwidth by reducing the size of piggybacked information. Finally, we relax several system-model assumptions, or replace them with practical ones, in order to improve the practicality of the proposed broadcast algorithm.
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