Efficient Time and Space Representation of Uncertain Event Data ⋆ Marco Pegoraro  [0000−0002−8997−7517] , Merih Seran Uysal [0000−0003−1115−6601] , and Wil M.P. van der Aalst [0000−0002−0955−6940] Process and Data Science Group (PADS) Department of Computer Science, RWTH Aachen University, Aachen, Germany {pegoraro, uysal, wvdaalst}@pads.rwth-aachen.de http://www.pads.rwth-aachen.de/ Abstract. Process mining is a discipline which concerns the analysis of execution data of operational processes, the extraction of models from event data, the measurement of the conformance between event data and normative models, and the enhancement of all aspects of processes. Most approaches assume that event data is accurately capture behavior. However, this is not realistic in many applications: data can contain un- certainty, generated from errors in recording, imprecise measurements, and other factors. Recently, new methods have been developed to an- alyze event data containing uncertainty; these techniques prominently rely on representing uncertain event data by means of graph-based mod- els explicitly capturing uncertainty. In this paper, we introduce a new approach to efficiently calculate a graph representation of the behavior contained in an uncertain process trace. We present our novel algorithm, prove its asymptotic time complexity, and show experimental results that highlight order-of-magnitude performance improvements for the behav- ior graph construction. Keywords: Process Mining · Uncertain Data · Partial Order. 1 Introduction The pervasive diffusion of digitization, which gained momentum thanks to ad- vancements in electronics and computing at the end of the last century, brought a wave of innovation in the tools supporting businesses and companies. The past decades have seen the rise of Process-Aware Information Systems (PAISs) – use- ful to structurally support processes in a business – as well as research disciplines such as Business Process Management (BPM) and process mining. Process mining [2] is a field of research that enables process analysis in a data-driven manner. Process mining analyses are based on recordings of tasks and events in a process, memorize in an ensemble of information systems which support business operations. These recordings are exported and systematically ⋆ We thank the Alexander von Humboldt (AvH) Stiftung for supporting our research interactions. Please do not print this document unless strictly necessary. arXiv:2010.00334v2 [cs.DS] 8 Nov 2020