Considerable amounts of data, including process event data, are collected and stored by organisations nowadays. Discovering a process model from recorded process event data is the aim of process discovery algorithms. Many techniques have been proposed, but none combines scalability with quality guarantees, e.g. can handle billions of events or thousands of activities, and produces sound models (without deadlocks and other anomalies), and guarantees to rediscover the underlying process in some cases. In this paper, we introduce a framework for process discovery that computes a directly-follows graph by passing over the log once, and applying a divide-and-conquer strategy. Moreover, we introduce three algorithms using the framework. We experi...