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In many body sensor network (BSN) applications, such as activity recognition for assisted living residents or physical fitness assessment of a sports team, users spend a significant amount of time with one another while performing many of the same activities. We exploit this physical proximity with Remora, a smartphone-based Body Sensor Network activity recognition system which shares sensing resources among neighboring BSNs. Compared to other resource sharing approaches, Remora provides both increased accuracy and significant energy savings. To increase classification accuracy, Remora BSNs share sensors by overhearing neighbors' sensor data transmissions. When sharing, fewer on-body sensors are needed to achieve high accuracy, resulting in energy savings by turning off unneeded sensors. To save phone energy, neighboring BSNs share classifiers: only one classifier is active at a time classifying activities for all neighbors. Remora addresses three major challenges of sharing with physical neighbors: 1) Sharing only when the energy benefit outweighs the cost, 2) Finding and utilizing the shared sensors and classifiers which produce the best combination of accuracy improvement and energy savings, and 3) Providing a lightweight and collaborative classification approach, without the use of a backend server, which adapts to the dynamics of available neighbors. In a two week evaluation with 6 subjects, we show that Remora provides up to a 30% accuracy increase while extending phone battery lifetime by over 65%.