## 4 Results and Discussion
### Real Case Study  
In order to assess the performance of the proposed approach against a real case study, we used a data mining workflow [27] that implements a model selection strategy for the classification of an unlabeled dataset. Figure 9 shows a representation of the workflow \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Strategy**} & \multirow{2}{*}{**Task-Scheduling Plan**} & **Number of Stages** & **Time (min)** & **Peak Disk Usage (MB)** & **Writes Duration (min)** & **On-Disk Usage (MB)** \\ \hline \multirow{3}{*}{Full-Parallel} & \(\begin{array}{c}(t_{0}),(t_{1}\parallel t_{2}\parallel t_{3}\parallel t_{4}),\\ (t_{5}\parallel t_{6}\parallel t_{7}\parallel t_{8}\parallel t_{9}\parallel t _{10}\parallel t_{11}\parallel t_{22}),\\ (t_{13}\parallel t_{4}\parallel t_{15}\parallel t_{6}\parallel t_{17} \parallel t_{8}\parallel t_{9}\parallel t_{20}),\\ (t_{21}),(t_{22}\parallel t_{23}\parallel t_{24}\parallel t_{25}),(t_{26}) \\ \end{array}\) & \multirow{3}{*}{7} & \multirow{3}{*}{29.42 \(\pm\) 1.88} & \multirow{3}{*}{27,095.84} & \multirow{3}{*}{20.6} & \multirow{3}{*}{10,593.79} \\ \cline{1-1} \cline{5-5}  & \(\begin{array}{c}(t_{0}),(t_{4}\parallel t_{2}),(t_{11}\parallel t_{7}),(t_{8 }\parallel t_{3}),\\ (t_{5}\parallel t_{10}\parallel t_{10}),(t_{16}),\\ (t_{17}\parallel t_{12}\parallel t_{20}\parallel t_{15}),(t_{14}),\\ (t_{31}\parallel t_{20}\parallel t_{19}),(t_{21}),\\ (t_{23}\parallel t_{24}),(t_{25}),(t_{22}),(t_{26})\\ \end{array}\) & \multirow{3}{*}{15} & \multirow{3}{*}{22.68 \(\pm\) 1.65} & \multirow{3}{*}{304.5} & \multirow{3}{*}{3.6} & \multirow{3}{*}{60.82} \\ \cline{1-1} \cline{5-5}  & \(\begin{array}{c}(t_{32}),(t_{23}),(t_{23}),(t_{24}),\\ (t_{32}\parallel t_{24}),\\ (t_{33}\parallel t_{24}),\\ \end{array}\) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Scheduling plan and statistics about execution times and disk usage with 9.5 GB of RAM. Figure 8: Disk usage over time for full-parallel and the IIWM. designed by the visual language VL4 Cloud [28]. The training set was divided into \(n\) partitions, and \(k\) classification algorithms were fit on each partition for generating \(k\times n\) classification models. The \(k\times n\) fit models were evaluated by a model selector on a test set to choose the best model. Afterwards, the \(n\) predictors used the best model to generate \(n\) classified datasets. The following \(k\) classification algorithms provided by the MLlib library were used: decision tree with C4.5 algorithm, Support Vector Machines (SVMs), and naive Bayes. The training set, test set, and unlabeled dataset provided as the input for the workflow were generated from the Physical Unclonable Functions (PUFs) [29] simulation through an \(n\)-fold-cross strategy. In this scenario, the IIWM can be used to optimize the data processing phase regarding the execution of the \(k\times n\) classification algorithms (estimators first, transformers second) concurrently. The other phases, such as data acquisition and partitioning, were outside our interest. The red box in Figure 9 shows the tasks of the workflow that were analyzed. Figure 10 shows disk occupancy over time with 14 GB of RAM. In this case as well, the IIWM avoided disk writes, while full-parallel registered a high level of disk usage. In particular, during the training phase, the parallel execution of the \(k\times n\) models (with \(k=3\) and \(n=5\)) saturated memory with 15 concurrent tasks and generated disk writes up to 124 GB. The results are detailed in Table 13, which shows a boost in execution time of almost 1.66\(\times\) (\(p_{imp}\)) and a 40% time reduction (\(m_{imp}\)) with respect to full-parallel. Figure 10: Disk usage over time for full-parallel and the IIWM. Figure 9: Ensemble learning workflow.