## 5 Result and Discussion
### Algorithms' Performance Based on an Empirical Evaluation
#### 5.4.2 Performance According to Model Complexity  
Process model derivation does not only depend on the log complexity, but also on the model complexity. This set of experiment evaluates how the strategies perform under different configurable process model topologies and different configurable node dependencies. Based on the original configurable process model, three configurable process models were built with different topological characteristics: models that only include \(\times\) and \(\wedge\) operator nodes, models that only include \(\times\) and \(\circ\) operator nodes and models that consider all operator nodes (\(\times\), \(\wedge\) and \(\circ\)). In addition, for each one of these three configurable process models, three different configurable node dependencies were created: independent, dependent and mixed (as described in Section 4.3). In total, there are nine different configurable process models \(Q_{i}^{n}\), where \(i=1,\ldots,9\); they are summarized in Table 9.  
Three different target models derived from each of these nine configurable process models were used for experimentation. Based on these 27 target models, 27 different event logs were simulated. In Table 9, they are represented as \(L_{i\_1}\), \(L_{i\_2}\) and \(L_{i\_3}\), for \(i=1,\ldots,9\).  
We applied the exhaustive, genetic and greedy strategies to all nine configurable process models with their corresponding three event logs. The results are shown in Table 9, including the computing time and the conformance metric. The computing time required for all strategies is shown in Figure 19, where the average computing time required for the three event logs created for each configurable process model is displayed.  
Figure 19a depicts how much time the exhaustive strategy requires to evaluate all possible configurations in order to derive the best process tree in each case. The results obtained suggest that if the configurable process model has parallelism, the computing time required to get a derived process model increases, such as in the case of models with topologies that contain \(\times\) and \(\wedge\) operators or \(\times\), \(\wedge\) and \(\circ\) operators. This is due to the conformance method requiring more time to handle parallelism, because the traces to be processed are usually longer [26]; whereas models with a topology that only contain \(\times\) and \(\circ\) operators require a lower computing time to derive a process model. It can be noticed that this is independent of the configurable node dependencies.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**A**} & \multicolumn{2}{c}{**B**} & \multicolumn{2}{c}{**C**} \\ \cline{3-8}  & **Log Complexity** & \begin{tabular}{c} **Time** \\ **(hhmm:ss)** \\ \end{tabular} & \begin{tabular}{c} **Conformance** \\ **Conformance** \\ \end{tabular} & \begin{tabular}{c} **Time** \\ **(hhmm:ss)** \\ \end{tabular} & \
\begin{tabular}{c} **Time** \\ **(hhmm:ss)** \\ \end{tabular} &
\begin{tabular}{c} **Conformance** \\ **(hmm:ss)** \\ \end{tabular} \\ \hline \multirow{5}{*}{exhaustive} & 50t 10-20 rep & 2:28:23 & 0.922 & 0.27:36 & 0.939 & 2:41:04 & 0.672 \\  & 100t 10-20 rep & 4:08:03 & 0.923 & 1:10:33 & 0.935 & 10:04:35 & 0.784 \\  & 500t 10-20 rep & 27:04 & 0.924 & 5:55:05 & 0.941 & 4:14:38 & 0.787 \\  & 100A similar behavior can be observed in Figure 19a for the genetic strategy and in Figure 19a for the greedy strategy. In all cases, more computing time is required when the configurable process models have parallelism, regardless of the configurable nodes dependencies.  
Figure 19a also depicts that the greedy strategy to derive a process model requires considerably less computing time than the other two strategies.