In this paper we consider the model of communication where wireless devices can either switch their radios off to save energy (and hence, can neither send nor receive messages), or switch their radios on and engage in communication. The problem has been extensively studied in practice, in the setting such as deployment and clock synchronization of wireless sensor networks – see, for example, [31,41,33,29,40]. The goal in these papers is different from the classic problem of radio broadcast, i.e. avoiding interference. Here, the goal is instead to minimize the use of the radio for both transmitting and receiving, and for most of the time to shut the radio down completely, as the radio even in listening mode consumes a lot of energy. We distill a clean theoretical formulation of minimizing radio use and present near-optimal solutions. Our base model ignores issues of communication interference, although we also extend the model to handle this requirement. We assume that nodes intend ...