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This paper presents general hardware-independent models and algorithms to automate the operation of droplet-based microfluidic systems. In these systems, discrete liquid volumes of typically less than 1 are transported across a planar array by dielectrophoretic or electrowetting effects for biochemical analysis. Unlike in systems based on continuous flow through channels, valves, and pumps, the droplet paths can be reconfigured on demand and even in real time. Algorithms that generate efficient sequences of control signals for moving one or many droplets from start to goal positions, subject to constraints such as specific features and obstacles on the array surface or limitations in the control circuitry, are developed. In addition, an approach toward automatic mapping of a biochemical analysis task onto a DMFS is investigated. Achieving optimality in these algorithms can be prohibitive for large-scale configurations because of the high asymptotic complexity of coordinating multiple moving droplets. Instead, these algorithms achieve a compromise between high runtime efficiency and a more limited nonglobal optimality in the generated control sequences.