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Task scheduling on multiprocessor computers with dynamically variable voltage and speed is investigated as combinatorial optimization problems, namely, the problem of minimizing schedule length with energy consumption constraint and the problem of minimizing energy consumption with schedule length constraint. The first problem has applications in general multiprocessor computing systems where energy consumption is an important concern and in mobile computers where energy conservation is a main concern. The second problem has applications in real-time multiprocessing systems where timing constraint is a major requirement. These problems emphasize the tradeoff between power and performance and are defined such that the power-performance product is optimized by fixing one factor and minimizing the other. It is found that both problems are equivalent to the sum of powers problem and can be decomposed into two subproblems, namely, scheduling tasks and determining power supplies. Such decomposition makes design and analysis of heuristic algorithms tractable. We analyze the performance of list scheduling algorithms and equal-speed algorithms and prove that these algorithms are asymptotically optimal. Our extensive simulation data validate our analytical results and provide deeper insight into the performance of our heuristic algorithms.