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Discovering Directly-Follows Graph Model for Acyclic Processes

Nikita Shaimov, Irina Lomazova, Alexey Mitsyuk

TL;DR

This paper tackles the problem that standard Directly-Follows Graph (DFG) discovery can introduce cycles when representing inherently acyclic processes. It proposes a compositional approach: partition an acyclic event log into DFG-acyclic sublogs, run a classical DFG discovery on each, and merge the resulting acyclic subgraphs while preventing cycles by allowing duplicate event labels. The merging uses a connectivity graph and a minimum Feedback Vertex Set (FVS) computation, with two variants (Naive and More Accurate) to trade speed for quality; it also extends merging to handle duplicate event names via a greedy renaming strategy. Empirical evaluation on real and artificial data shows cycle-free, precise merged models with fitness comparable to standard DFGs but higher precision, at the cost of larger models and longer merge times. This approach enables clearer visualizations and cycle-sensitive analyses, and points to future work including applying the method to other notations and improving merge efficiency.

Abstract

Process mining is the common name for a range of methods and approaches aimed at analysing and improving processes. Specifically, methods that aim to derive process models from event logs fall under the category of process discovery. Within the range of processes, acyclic processes form a distinct category. In such processes, previously performed actions are not repeated, forming chains of unique actions. However, due to differences in the order of actions, existing process discovery methods can provide models containing cycles even if a process is acyclic. This paper presents a new process discovery algorithm that allows to discover acyclic DFG models for acyclic processes. A model is discovered by partitioning an event log into parts that provide acyclic DFG models and merging them while avoiding the formation of cycles. The resulting algorithm was tested both on real-life and artificial event logs. Absence of cycles improves model visual clarity and precision, also allowing to apply cycle-sensitive methods or visualisations to the model.

Discovering Directly-Follows Graph Model for Acyclic Processes

TL;DR

This paper tackles the problem that standard Directly-Follows Graph (DFG) discovery can introduce cycles when representing inherently acyclic processes. It proposes a compositional approach: partition an acyclic event log into DFG-acyclic sublogs, run a classical DFG discovery on each, and merge the resulting acyclic subgraphs while preventing cycles by allowing duplicate event labels. The merging uses a connectivity graph and a minimum Feedback Vertex Set (FVS) computation, with two variants (Naive and More Accurate) to trade speed for quality; it also extends merging to handle duplicate event names via a greedy renaming strategy. Empirical evaluation on real and artificial data shows cycle-free, precise merged models with fitness comparable to standard DFGs but higher precision, at the cost of larger models and longer merge times. This approach enables clearer visualizations and cycle-sensitive analyses, and points to future work including applying the method to other notations and improving merge efficiency.

Abstract

Process mining is the common name for a range of methods and approaches aimed at analysing and improving processes. Specifically, methods that aim to derive process models from event logs fall under the category of process discovery. Within the range of processes, acyclic processes form a distinct category. In such processes, previously performed actions are not repeated, forming chains of unique actions. However, due to differences in the order of actions, existing process discovery methods can provide models containing cycles even if a process is acyclic. This paper presents a new process discovery algorithm that allows to discover acyclic DFG models for acyclic processes. A model is discovered by partitioning an event log into parts that provide acyclic DFG models and merging them while avoiding the formation of cycles. The resulting algorithm was tested both on real-life and artificial event logs. Absence of cycles improves model visual clarity and precision, also allowing to apply cycle-sensitive methods or visualisations to the model.

Paper Structure

This paper contains 16 sections, 15 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Motivating example
  3. Basic definitions
  4. Acyclic DFG model discovery
  5. Acyclic event log partitioning
  6. Merging algorithm for two acyclic DFG models
  7. Naive Approach
  8. More Accurate Merging
  9. Merging two acyclic DFG models with duplicate event names
  10. Evaluation
  11. Real-life case description
  12. Models examples
  13. Models assessment
  14. Artificial data
  15. Related work
  16. ...and 1 more sections

Figures (15)

  • Figure 1: An example DFG with cycles
  • Figure 2: The DFG corresponding to the log shown in Table \ref{['tbl:example']}
  • Figure 3: Compositionality of the "perfect fitness" ("$\downarrow$") relation
  • Figure 4: Two DFGs with three common subgraphs: vertices $A$, $B$, and $C$ form the first subgraph; $F$, $G$, and $H$ --- the second one; and vertices $J$, $K$ --- the third one
  • Figure 5: Connectivity graph with three subgraphs as nodes
  • ...and 10 more figures

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5