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While improving raw performance is of primary interest to most users of high-performance computers, energy consumption also is a critical concern. Some microprocessors allow voltage and frequency scaling, which enables a system to reduce CPU power and performance when the CPU is not on the critical path. When properly directed, such dynamic voltage and frequency scaling can produce significant energy savings with little performance penalty. Various DVFS scaling algorithms have been proposed. However, the benefit is application-dependent. We cannot see if they achieve the energy consumption as minimum as possible. So, it is important to establish the baseline of the DVFS scheduling for any application. This paper determines minimum energy consumption in voltage and frequency scaling systems for a given time delay. We assume we have a set of fixed points where scaling can occur. A brute-force solution is intractable even for a moderately sized set (although all programs presented in this paper can be solved with the brute-force). Our algorithm efficiently chooses the exact optimal schedule satisfying the given time constraint by estimation. Besides, our time and energy estimations from the optimal schedule have reasonable accuracy with 1.48% of differences at maximum.