## 4 Experiment Evaluations
### Rmo_SODSDA Efficiency  
#### 4.2.1 Datasets and Experiment Setup  
Datasets: according to Table 6, the number of the chosen roles in the second group of experiments increased from 40 to 300 with a step of 20. In addition, the QMaxSAT solver was chosen because it performed quite well in the latest MAX-SAT evaluation and because of its efficiency on sets of encoding clauses. Clauses updated based on truth assignments were written in Java. Experiment setup: for the given UAQ \(<s\), \(P_{lb}\), \(P_{ub}\), \(match\)\(>\), \(s\) is a session in \(S\), \(Pu\) represents permissions assigned to user \(u\) in our constructed RBAC system, and \(Prequest\subseteq Pu\). This can be obtained using Sat4j 2.3.4 (April 2013), an open-source satisfiability library in Java [(40)]. We considered \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 30**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 50**} \\ \cline{2-7}  & \(C_{\text{2-2 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{2-2 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) \\ \hline Americas-large & 2022.7 s & 2054.3 s & 1314.7 s & 5762.9 s & 5861.9 s & 3751.6 s \\ Americas-small & 117.7 s & 143.6 s & 91.9 s & 280.9 s & 337.9 s & 216.2 s \\ Apj & 6.7 s & 7.1 s & 4.5 s & 17.9 s & 19.7 s & 12.6 s \\ Customer & 1.2 s & 5.0 s & 3.2 s & 2.7 s & 12.1 s & 7.7 s \\ Emea & 0.3 s & 0.3 s & 0.2 s & 0.8 s & 0.8 s & 0.5 s \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Execution time with 5–10 RSSOD. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 30**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 50**} \\ \cline{2-7}  & \(C_{\text{2-2 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{2-2 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) \\ \hline Americas-large & 139.7 s & 144.7 s & 289.5 s & 366.2 s & 379.5 s & 759.1 s \\ Americas-small & 10.1 s & 10.1 s & 20.2 s & 29.2 s & 30.2 s & 60.4 s \\ Apj & 0.3 s & 0.4 s & 0.8 s & 0.9 s & 1.2 s & 2.4 s \\ Customer & 0.01 s & 0.2 s & 0.4 s & 0.01 s & 0.5 s & 1.1 s \\ Emea & 0.02 s & 0.02 s & 0.04 s & 0.05 s & 0.06 s & 0.12 s \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Execution time with 2–2 RSSOD. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 30**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 50**} \\ \cline{2-7}  & \(C_{\text{2-2 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) \\ \hline Americas-large & 2022.7 s & 2054.3 s & 1314.7 s & 5762.9 s & 5861.9 s & 3751.6 s \\ Americas-small & 117.7 s & 143.6 s & 91.9 s & 280.9 s & 337.9 s & 216.2 s \\ Apj & 6.7 s & 7.1 s & 4.5 s & 17.9 s & 19.7 s & 12.6 s \\ Customer & 1.2 s & 5.0 s & 3.2 s & 2.7 s & 12.1 s & 7.7 s \\ Emea & 0.3 s & 0.3 s & 0.2 s & 0.8 s & 0.8 s & 0.5 s \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Execution time with 3–5 RSSOD. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 30**} & \multicolumn{3}{c}{\(|E_{\text{2-2 RSSOD}}|\)**= 50**} \\ \cline{2-7}  & \(C_{\text{2-2 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) & \(C_{\text{1-4 SMER}}\) \\ \hline Americas-large & 139.7 s & 144.7 s & 289.5 s & 366.2 s & 379.5 s & 759.1 s \\ Americas-small & 10.1 s & 10.1 s & 20.2 s & 29.2 s & 30.2 s & 60.4 s \\ Apj & 0.3 s & 0.4 s & 0.8 s & 0.9 s & 1.2 s & 2.4 s \\ Customer & 0.01 s & 0.2 s & 0.4 s & 0.01 s & 0.5 s & 1.1 s \\ Emea & 0.02 s & 0.02 s & 0.04 s & 0.05 s & 0.06 s & 0.12 s \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Execution time with 2–3 RSSOD.