We consider the problem of multicasting from a single source to a set of destinations. We assume that the source can either reach the destinations directly or forward its traffic through a set of relays. Due to the non-linear attenuation of the signal with distance, employing the relays can help to improve the signal quality at the destinations. Meanwhile, relays also consume energy for retransmission of the received information and the rate of communication can be decreased due to the multi-hop transmission. Under the performance objective of maximizing the common amount of information (number of bits) that the source sends to all destinations per Joule of the total energy spent, we wish to identify whether direct transmission from the source to the destinations is preferable as opposed to multi-hop forwarding through the relays. In the latter case, we also identify a) which subset of the relays should be activated, b) for how long, and c) the respective destinations that each relay has to serve. Finally, we provide a set of numerical results to support our analysis.
