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Task Scheduling with Dynamic Voltage and Frequency Scaling for Energy Minimization in the Mobile Cloud Computing Environment Mobile cloud computing (MCC) offers significant opportunities in performance enhancement and energy saving for mobile, battery-powered devices. Applications running on mobile devices may be represented by task graphs. This work investigates the problem of scheduling tasks (which belong to the same or possibly different applications) in the MCC environment. More precisely, the scheduling problem involves the following steps: (i) determining the tasks to be offloaded onto the cloud, (ii) mapping the remaining tasks onto (potentially heterogeneous) local cores in the mobile device, (iii) determining the frequencies for executing local tasks, and (iv) scheduling tasks on the cores (for in-house tasks) and the wireless communication channels (for offloaded tasks) such that the task-precedence requirements and the application completion time constraint are satisfied while the total energy dissipation in the mobile device is minimized. A novel algorithm is presented, which starts from a minimal-delay scheduling solution and subsequently performs energy reduction by migrating tasks among the local cores and the cloud and by applying the dynamic voltage and frequency scaling technique. A linear-time rescheduling algorithm is proposed for the task migration. Simulation results demonstrate significant energy reduction with the application completion time constraint satisfied.