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Design systems to provide various quality of service (QoS) guarantees have received a lot of attention due to the increasing popularity of real-time multimedia and wireless communication applications. Meanwhile, low power consumption is always one of the goals for system design, especially for battery-operated systems. With the design trend of integrating multiple processor cores and memory on a single chip, we address the problem of how to partition a set of applications among processors, such that all the individual QoS requirements are met and the total energy consumption is minimized. We exploit the advantages provided by the variable voltage design methodology to choose the voltage for each application on the same processor optimally for this purpose. We also discuss how to partition applications among the processors to achieve the same goal. We formulate the problem on an abstract QoS model and present how to allocate resources (e.g., CPU time) and determine the voltage profile for every single processor. Experiments on media benchmarks have also been studied.