Oblivious k-shot Broadcasting in Ad Hoc Radio Networks

We study distributed broadcasting protocols with few transmissions (‘shots’) in radio networks of unknown topology. In particular, we examine the case in which a bound k is given and a node may transmit at most k times during the broadcasting protocol. We focus on oblivious algorithms, that is, algorithms where each node decides whether to transmit or not with no consideration of the transmission history. Our main contributions are (a) a lower bound of Ω( 2 k ) on the broadcasting time of any oblivious k-shot broadcasting algorithm and (b) an oblivious broadcasting protocol that achieves a matching upper bound, namely O( 2 k ), for every k ≤ √ n and an upper bound of O(n) for every k > √ n. We also initiate the study of the behavior of general broadcasting protocols by showing an Ω(n) lower bound for any adaptive 1-shot broadcasting protocol.