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eST$^2$ Miner -- Process Discovery Based on Firing Partial Orders

Sabine Folz-Weinstein, Christian Rennert, Lisa Luise Mannel, Robin Bergenthum, Wil van der Aalst

TL;DR

The paper tackles the limitations of using totally ordered event logs for process discovery by enabling direct processing of partially ordered inputs. It presents the eST$^2$ Miner, a fusion of the eST Miner and the Firing LPO algorithm, to derive workflow nets from labeled partial orders via compact tokenflows, using forward/backward heuristics and a max-flow step with worst-case $\mathcal{O}(n^3)$ complexity. The approach retains the strong guarantees of the eST Miner while offering improved applicability and efficiency on real-life, concurrent processes, as demonstrated on public and private logs with near-linear runtime improvements over the totally ordered baseline. This work advances practical partial-order based process mining and lays groundwork for future comparisons with other concurrency-aware discovery methods across domains like healthcare, education, and logistics.

Abstract

Process discovery generates process models from event logs. Traditionally, an event log is defined as a multiset of traces, where each trace is a sequence of events. The total order of the events in a sequential trace is typically based on their temporal occurrence. However, real-life processes are partially ordered by nature. Different activities can occur in different parts of the process and, thus, independently of each other. Therefore, the temporal total order of events does not necessarily reflect their causal order, as also causally unrelated events may be ordered in time. Only partial orders allow to express concurrency, duration, overlap, and uncertainty of events. Consequently, there is a growing need for process mining algorithms that can directly handle partially ordered input. In this paper, we combine two well-established and efficient algorithms, the eST Miner from the process mining community and the Firing LPO algorithm from the Petri net community, to introduce the eST$^2$ Miner. The eST$^2$ Miner is a process discovery algorithm that can directly handle partially ordered input, gives strong formal guarantees, offers good runtime and excellent space complexity, and can, thus, be used in real-life applications.

eST$^2$ Miner -- Process Discovery Based on Firing Partial Orders

TL;DR

The paper tackles the limitations of using totally ordered event logs for process discovery by enabling direct processing of partially ordered inputs. It presents the eST Miner, a fusion of the eST Miner and the Firing LPO algorithm, to derive workflow nets from labeled partial orders via compact tokenflows, using forward/backward heuristics and a max-flow step with worst-case complexity. The approach retains the strong guarantees of the eST Miner while offering improved applicability and efficiency on real-life, concurrent processes, as demonstrated on public and private logs with near-linear runtime improvements over the totally ordered baseline. This work advances practical partial-order based process mining and lays groundwork for future comparisons with other concurrency-aware discovery methods across domains like healthcare, education, and logistics.

Abstract

Process discovery generates process models from event logs. Traditionally, an event log is defined as a multiset of traces, where each trace is a sequence of events. The total order of the events in a sequential trace is typically based on their temporal occurrence. However, real-life processes are partially ordered by nature. Different activities can occur in different parts of the process and, thus, independently of each other. Therefore, the temporal total order of events does not necessarily reflect their causal order, as also causally unrelated events may be ordered in time. Only partial orders allow to express concurrency, duration, overlap, and uncertainty of events. Consequently, there is a growing need for process mining algorithms that can directly handle partially ordered input. In this paper, we combine two well-established and efficient algorithms, the eST Miner from the process mining community and the Firing LPO algorithm from the Petri net community, to introduce the eST Miner. The eST Miner is a process discovery algorithm that can directly handle partially ordered input, gives strong formal guarantees, offers good runtime and excellent space complexity, and can, thus, be used in real-life applications.

Paper Structure

This paper contains 7 sections, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Replay-Based Process Discovery
  4. The $\text{eST}^2$ Miner
  5. Evaluation
  6. Conclusion
  7. Acknowledgments.

Figures (4)

  • Figure 1: Example event log with three traces. Each trace is a sequence of courses taken by one student, totally ordered based on course exam dates.
  • Figure 2: Partially ordered representation of the three traces in Figure \ref{['fig:edutotal']}.
  • Figure 3: A workflow net (top) and a labeled partial order with a compact tokenflow for p4 (bottom).
  • Figure 4: High-level overview of the $\text{eST}^2$ Miner framework.

Theorems & Definitions (4)

  • definition thmcounterdefinition: Labeled Partial Order, lpo
  • definition thmcounterdefinition: Event Log
  • definition thmcounterdefinition: Workflow Net
  • definition thmcounterdefinition: Behavior of a Workflow Net