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Offloading traffic through opportunistic communications has been recently proposed as a way to relieve the current overload of cellular networks. Opportunistic communication can occur when mobile device users are (temporarily) in each other's proximity, such that the devices can establish a local peer-to-peer connection (e.g., via WLAN or Bluetooth). Since opportunistic communication is based on the spontaneous mobility of the participants, it is inherently unreliable. This poses a serious challenge to the design of any cellular offloading solutions, that must meet the applications' requirements. In this paper, we address this challenge from an optimization analysis perspective, in contrast to the existing heuristic solutions. We first model the dissemination of content (injected through the cellular interface) in an opportunistic network with heterogeneous node mobility. Then, based on this model, we derive the optimal …