In this paper, a novel algorithm is proposed for assigning supply voltages to serially executing functional units (FUs) in a digital system such that the overall dynamic energy consumption is minimized for a given timing constraint. Novel closed form expressions for optimum supply voltage values are presented. The computation time of the algorithm is O(N)for N FUs in series. An extension of the O(N) algorithm is proposed for optimizing the acyclic data flow graph associated with any given task. Given the number of FUs available for the task, the operations required for the task are scheduled on the FUs. Voltages are then assigned to the FUs on each path of the flow graph using the O(N) algorithm. Energy savings of 10-60% are achieved on DSP filter designs using the proposed high-level optimization methodology over single supply voltage designs.