Abstract
The alignment of observed and modeled behavior is a crucial problem in process mining, since it opens the door for conformance checking and enhancement of process models. The state of the art techniques for the computation of alignments rely on a full exploration of the combination of the model state space and the observed behavior (an event log), which hampers their applicability for large instances. This paper presents a fresh view to the alignment problem: the computation of alignments is casted as the resolution of Integer Linear Programming models, where the user can decide the granularity of the alignment steps. Moreover, a novel recursive strategy is used to split the problem into small pieces, exponentially reducing the complexity of the ILP models to be solved. The contributions of this paper represent a promising alternative to fight the inherent complexity of computing alignments for large instances.
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Notes
- 1.
There is no fundamental difference between aligning Petri nets or process trees: only the latter allows for a slightly better memory representation.
- 2.
\(\mathcal{B}(A)\) denotes the set of all multisets of the set A.
- 3.
The theory of this paper can deal with models having silent transitions. For the sake of simplicity, we do not consider them in the formalization.
- 4.
\(X \Delta Y = (X \setminus Y) \cup (Y \setminus X\)).
- 5.
In our experiments, only the simplest cases were encountered.
- 6.
Note the different way the traces are obtained, e.g., in the right part \(\text {tr}(X^s_2)\) is the leftmost part since it denotes log moves that the model can produce on the left step.
- 7.
The experiments have been done on a desktop computer with Intel Core i7-2.20 GHz, and 5 GB of RAM. Source code and benchmarks can be provided by contacting the first author.
- 8.
In spite of using \(\eta =1\), still the objects computed by our technique and the technique from [1] are different, and hence this comparison is only meant to provide an estimation on the speedup/memory/quality one can obtain by opting for approximate alignments.
- 9.
The plugin “Replay a log on Petri net for conformance analysis” from ProM with parameters “\(A^*\) cost-based fitness express with/without ILP and being/not being swap+replacement aware”. We instructed the techniques from [1] to compute one-optimal alignment.
- 10.
Most of the realistic benchmarks in Table 2 have silent transitions.
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Acknowledgments
This work was supported by the Spanish Ministry for Economy and Competitiveness (MINECO) and the European Union (FEDER funds) under grant COMMAS (ref. TIN2013-46181-C2-1-R).
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Taymouri, F., Carmona, J. (2016). A Recursive Paradigm for Aligning Observed Behavior of Large Structured Process Models. In: La Rosa, M., Loos, P., Pastor, O. (eds) Business Process Management. BPM 2016. Lecture Notes in Computer Science(), vol 9850. Springer, Cham. https://doi.org/10.1007/978-3-319-45348-4_12
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