Timed Alignments with Mixed Moves

We study conformance checking for timed models, that is, process models that consider both the sequence of events that occur, as well as the timestamps at which each event is recorded. Time-aware process mining is a growing subfield of research, and as tools that seek to discover timing-related properties in processes develop, so does the need for conformance-checking techniques that can tackle time constraints and provide insightful quality measures for time-aware process models. One of the most useful conformance artefacts is the alignment, that is, finding the minimal changes necessary to correct a new observation to conform to a process model. In this paper, we solve the timed alignment problem where the metrics used to compare timed processes allow weighted mixed moves, i.e. an error on the timestamp of an event may or may not propagate to its successors, and we provide linear time algorithms for a large class of such weighted mixed distances, both for distance computation and alignment on models with sequential causal processes.