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In this paper, a new power saving mechanism in delay/disruption tolerant networks is designed. By exploiting the intermittent connection characteristic of delay/disruption tolerant network in synchronized clock based scenario, an adaptive exponential beacon protocol is proposed where the beacon periods of nodes are independently adjusted depending on the trend of contact availability. The proposed protocol is optimized for different network environments using distribution of contact durations. Simulation results show that power savings up to 35 percent are achieved compared with existing power saving protocols, while maintaining similar average packet delays and packet delivery ratios to that without a power management.