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Offloading is an effective method for extending the lifetime of handheld mobile devices by executing some components of applications remotely (e.g., on the server in a data center or in a cloud). In this article, to achieve energy saving while satisfying given application execution time requirement, we present a dynamic offloading algorithm, which is based on Lyapunov optimization. The algorithm has low complexity to solve the offloading problem (i.e., to determine which software components to execute remotely given available wireless network connectivity). Performance evaluation shows that the proposed algorithm saves more energy than the existing algorithm while meeting the requirement of application execution time.