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Contact discovery is a fundamental premise of information exchange in delay-tolerant networks (DTNs). However, the intermittent connectivity nature of DTNs makes energy-efficient contact discovery a tough challenge. To save energy, a node should work in low-power mode most of the time since contacts with the other nodes may rarely happen. However, such a strategy will probably fail to detect many contacts with relatively short durations, leading to system performance degradation. In this paper, we consider a specific type of DTN, i.e., the pocket switched networks (PSN), in which the nodes' mobility pattern shows a strong social property. In a PSN, although the end-to-end path may be disconnected for the majority of time, several nodes periodically gather at certain hot spots and form well-connected clusters. Based on such mobility pattern, cooperation among nodes is utilized in our contact discovery design. The nodes that have already joined a cluster collaboratively wake up to discover new contacts. With local synchronization and complementary consideration of possible traffic congestion, both the theoretical analysis and simulation results show that our cooperative duty cycling (CDC) greatly reduces the energy consumption while achieving comparable data delivery performance.