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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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.
References
Adriansyah, A.: Aligning observed and modeled behavior. Ph.D. thesis, Technische Universiteit Eindhoven (2014)
Adriansyah, A., Munoz-Gama, J., Carmona, J., van Dongen, B.F., van der Aalst, W.M.P.: Measuring precision of modeled behavior. Inf. Syst. E-Bus. Manag. 13(1), 37–67 (2015)
Buijs, J.C.A.M.: Flexible evolutionary algorithms for mining structured process models. Ph.D. thesis, Technische Universiteit Eindhoven (2014)
Desel, J., Esparza, J.: Reachability in cyclic extended free-choice systems. TCS 114, 93–118 (1993). Elsevier Science Publishers B.V
Esparza, J., Melzer, S.: Verification of safety properties using integer programming: beyond the state equation. Formal Methods Syst. Des. 16, 159–189 (2000)
Fahland, D., van der Aalst, W.M.P.: Model repair - aligning process models to reality. Inf. Syst. 47, 220–243 (2015)
Leemans, S.J.J., Fahland, D., van der Aalst, W.M.P.: Scalable process discovery with guarantees. In: Gaaloul, K., Schmidt, R., Nurcan, S., Guerreiro, S., Ma, Q. (eds.) BPMDS 2015 and EMMSAD 2015. LNBIP, vol. 214, pp. 85–101. Springer, Heidelberg (2015)
Xixi, L., Fahland, D., van der Aalst, W.M.P.: Conformance checking based on partially ordered event data. In: Business Process Management Workshops - BPM 2014 International Workshops, Eindhoven, The Netherlands, 7–8 September 2014, Revised Papers, pp. 75–88 (2014)
Xixi, L., Mans, R., Fahland, D., van der Aalst, W.M.P.: Conformance checking in healthcare based on partially ordered event data. In: Proceedings of the 2014 IEEE Emerging Technology and Factory Automation, ETFA 2014, Barcelona, Spain, 16–19 September 2014, pp. 1–8 (2014)
Munoz-Gama, J., Carmona, J., van der Aalst, W.M.P.: Single-entry single-exit decomposed conformance checking. Inf. Syst. 46, 102–122 (2014)
Murata, T.: Petri nets: Properties, analysis and applications. Proc. IEEE 77(4), 541–574 (1989)
Silva, M., Teruel, E., Colom, J.M.: Linear algebraic and linear programming techniques for the analysis of place/transition net systems. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491. Springer, Heidelberg (1998)
van der Aalst, W.M.P.: Process Mining - Discovery: Conformance and Enhancement of Business Processes. Springer, Heidelberg (2011)
van der Aalst, W.M.P.: Decomposing petri nets for process mining: a generic approach. Distrib. Parallel Databases 31(4), 471–507 (2013)
vanden Broucke, S.K.L.M., Munoz-Gama, J., Carmona, J., Baesens, B., Vanthienen, J.: Event-based real-time decomposed conformance analysis. In: Meersman, R., Panetto, H., Dillon, T., Missikoff, M., Liu, L., Pastor, O., Cuzzocrea, A., Sellis, T. (eds.) OTM 2014. LNCS, vol. 8841, pp. 345–363. Springer, Heidelberg (2014)
De Weerdt, J., vanden Broucke, K.L.M., Vanthienen, J., Baesens, B.: Active trace clustering for improved process discovery. IEEE Trans. Knowl. Data Eng. 25(12), 2708–2720 (2013)
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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-45348-4_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45347-7
Online ISBN: 978-3-319-45348-4
eBook Packages: Computer ScienceComputer Science (R0)