Process mining aims to understand the actual behavior and performance of business processes from event logs recorded by IT systems. A key requirement is that every event in the log must be associated with a unique case identifier (e.g., the order ID in an order-to-cash process). In reality, however, this case ID may not always be present, especially when logs are acquired from different systems or when such systems have not been explicitly designed to offer process-tracking capabilities. Existing techniques for correlating events have worked with assumptions to make the problem tractable: some assume the generative processes to be acyclic while others require heuristic information or user input. In this paper, we lift these assumptions by presenting a novel technique called EC-SA based on probabilistic optimization. Given as input a sequence of timestamped events (the log without case IDs) and a process model describing the underlying business process, our approach returns an event log in which every event is mapped to a case identifier. The approach minimises the misalignment between the generated log and the input process model, and the variance between activity durations across cases. The experiments conducted on a variety of real-life datasets show the advantages of our approach over the state of the art.

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