Energy-efficient broadcasting in ad hoc wireless networks

We study energy-efficient broadcasting in wireless networks of unknown topology (ad hoc). We measure energy efficiency by the maximum number of transmissions ('shots') allowed to any node in the network. 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 at each step 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(n2/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(n2/k), for every k≤n and an upper bound of O(n3/2) 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 to each. We prove a lower bound of Ω(n1+kk) on the broadcasting time of any protocol by introducing the transmission tree construction which generalizes previous approaches.