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We present Dionysus, a system for fast, consistent network updates in software-defined networks. Dionysus encodes as a graph the consistency-related dependencies among updates at individual switches, and it then dynamically schedules these updates based on runtime differences in the update speeds of different switches. This dynamic scheduling is the key to its speed; prior update methods are slow because they pre-determine a schedule, which does not adapt to runtime conditions. Testbed experiments and data-driven simulations show that Dionysus improves the median update speed by 53-88% in both wide area and data center networks compared to prior methods.