k-shot Broadcasting in Ad Hoc Radio Networks

We study distributed broadcasting protocols with few transmissions (‘shots’) in radio networks where the topology is unknown. 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. Initially, we focus on oblivious algorithms for k-shot broadcasting, 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(n/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(n/k), for every k ≤ √ n and an upper bound of O(n) for every k > √ n. We also study the general case of adaptive broadcasting protocols where nodes decide whether to transmit based on all the available information, namely the transmission history known by each. We prove a lower bound of Ω ( n 1+k k ) on the broadcasting time of any protocol by introducing the transmission tree construction which generalizes previous approaches.