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An integer linear programming model to improve the dependency graph discovery step of heuristics miner methods

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Abstract

Heuristic mining techniques are among the most popular methods in the process discovery area. This category of methods is composed of two main steps: (1) discovering a dependency graph and (2) determining the split/join patterns of the dependency graph. The current dependency graph discovery techniques of heuristic-based methods select the initial set of graph arcs according to dependency measures and then modify the set regarding some criteria. This can lead to selecting the non-optimal set of arcs. Also, the modifications can result in modeling rare behaviors and, consequently, low precision and non-simple process models. The motivation of this paper is to improve the heuristic mining methods by addressing the mentioned issues. The contribution of this paper is to propose a new integer linear programming model that determines the optimal set of graph arcs regarding dependency measures. Simultaneously, the proposed method can eliminate some other issues that the existing methods cannot handle completely; i.e., even in the presence of loops, it guarantees that all tasks are on a path from the initial to the final tasks. This approach also allows utilizing domain knowledge by introducing appropriate constraints, which can be a practical advantage in real-world problems. To assess the results, we modified two existing methods of evaluating process models to make them capable of measuring the quality of dependency graphs. According to assessments, the proposed method’s outputs are superior to those of the most prominent dependency graph discovery methods in terms of fitness, precision, and especially simplicity.

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Authors and Affiliations

  1. School of Industrial Engineering, Iran University of Science and Technology, Tehran, 16844, Iran

    Maryam Tavakoli-Zaniani, Mohammad Reza Gholamian & Mehdi Ghazanfari

  2. Computer Engineering and IT Department, Amirkabir University of Technology, Tehran, 15875, Iran

    S. Alireza Hashemi Golpayegani

Authors
  1. Maryam Tavakoli-Zaniani
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  2. Mohammad Reza Gholamian
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  3. S. Alireza Hashemi Golpayegani
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Correspondence to Mohammad Reza Gholamian.

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Appendix A: Details on achieving FiM measure and \(F^L(x,y)\) value (required for calculating PrM measure

Appendix A: Details on achieving FiM measure and \(F^L(x,y)\) value (required for calculating PrM measure

Assuming an event log L and a dependency graph DG , the following definitions are used in the procedure of replaying L on DG:

  • \(\varepsilon \): The set of all events that are present in L.

  • \(A_L\): The set of tasks that are present in L.

  • \(A_{DG}\): The set of tasks that are present in DG.

  • \(T_L\): The set of traces that are present in L.

  • \(E:t \in T_L \mapsto E_t \subseteq \varepsilon \): The set of events that are present in t.

  • \(\delta :a \in A_L \mapsto A_{DG}\): The member of \(A_{DG}\) that corresponds to \(a \in A_L\).

  • \(Act :e_i \in \varepsilon \mapsto a \in A_L\): The member of \(A_L\) that corresponds to event \(e_i \in \varepsilon \).

  • \(inp : a \in A_{DG} \mapsto i_a \subseteq A_{DG}\): The set of tasks that according to DG are pre-requisite of \(a \in A_{DG}\).

  • \(out : a \in A_{DG} \mapsto o_a \subseteq A_{DG}\): The set of tasks that according to DG are post-requisite of \(a \in A_{DG}\).

  • \(pre: e_i \in E(t) \mapsto a_{pr} \subseteq A_L\): The sequence of tasks which are mapped to the sequence of all events present in t that occurred before \(e_i\).

  • \(suc: e_i \in E(t) \mapsto a_{po} \subseteq A_L\): The sequence of tasks which are mapped to the sequence of all events present in t that occurred after \(e_i\).

The pseudo-code of the proposed procedure for replaying L on DG and achieving FiM measure is explained in Algorithm 1, whereas the pseudo-code for calculating \(F^L(x,y)\) is presented in Algorithm 2.

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Tavakoli-Zaniani, M., Gholamian, M.R., Golpayegani, S.A.H. et al. An integer linear programming model to improve the dependency graph discovery step of heuristics miner methods. Knowl Inf Syst 65, 2087–2121 (2023). https://doi.org/10.1007/s10115-022-01821-2

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