In this paper we consider a new 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. Our goal is to minimize use of the radio for both transmitting and receiving. Our base model ignores issues of communication interference, though we also extend it to handle this requirement as well. We assume that nodes eventually intend to communicate periodically, or according to some other time-based schedule. Clearly, perfectly synchronized devices could switch their radios on for exactly the minimum periods required by their joint schedules. The main challenge is thus how to synchronize the devices ’ schedules, given that their initial schedules may be offset relative to one another (even if their clocks run at the same speed). In this paper we study how frequently the devices must switch on their radios in order to both synchronize their clocks and communicate. The abstract problem is new even for two processors. In this setting, we show optimal use of the radio for two processors and near-optimal use of the radio for synchronization of an arbitrary number of processors. In particular, for two processors we prove a tight (up to constant factors) matching Θ ( √ n) upper and lower bounds of the number of times the radio has to be on, where n is the discretized uncertainty perio
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