Timed alignments with mixed moves

Abstract

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 extend the notion of timed distance from a previous work where an edit on an event’s timestamp came in two types, depending on whether or not it would propagate to its successors. Here, these different types of edits have a weighted cost each, and the ratio of their costs is denoted by $\alpha$. We then solve the purely timed alignment problem in this setting for a large class of these weighted distances (corresponding to $\alpha \in \left\{1\right\}\cup [2,\infty )$). For these distances, we provide linear time algorithms for both distance computation and alignment on models with sequential causal processes.