+\subsection{The comparison of the proposed scaling algorithm }
+\label{sec.compare_EDP}
+
+In this section, the scaling factors selection algorithm
+is compared to Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}.
+They developed a green governor that regularly applies an online frequency selecting algorithm to reduce the energy consumed by a multicore architecture without degrading much its performance. The algorithm selects the frequencies that minimize the energy and delay products, $EDP=Enegry*Delay$ using the predicted overall energy consumption and execution time delay for each frequency.
+ To fairly compare both algorithms, the same energy and execution time models, equations (\ref{eq:energy}) and (\ref{eq:fnew}), were used for both algorithms to predict the energy consumption and the execution times. Also Spiliopoulos et al. algorithm was adapted to start the search from the
+initial frequencies computed using the equation (\ref{eq:Fint}). The resulting algorithm is an exhaustive search algorithm that minimizes the EDP and has the initial frequencies values as an upper bound.
+
+Both algorithms were applied to the parallel NAS benchmarks to compare their efficiency. Table \ref{table:compare_EDP} presents the results of comparing the execution times and the energy consumptions for both versions of the NAS benchmarks while running the class C of each benchmark over 8 or 9 heterogeneous nodes. \textcolor{red}{The results show that our algorithm gives better energy savings than Spiliopoulos et al. algorithm,
+on average it is up to 17\% higher for energy saving compared to their algorithm. The average of performance degradation percentage using our method is higher on average by 3.82\%. The positive values for energy saving and distance are mean that our method outperform Spiliopoulos et al. method, while the inverse is happen for the negative values. The negative values for performance degradation percentage are mean our method is has the less delay in time, while the positive values mean the inverse. }
+
+For all benchmarks, our algorithm outperforms
+Spiliopoulos et al. algorithm in term of energy and performance tradeoff \textcolor{red}{(on average it has up to 21\% of distance)}, see figure (\ref{fig:compare_EDP}) because it maximizes the distance between the energy saving and the performance degradation values while giving the same weight for both metrics.
+\begin{table}[h]
+ \caption{Comparing the proposed algorithm}
+ \centering
+\begin{tabular}{|l|l|l|l|l|l|l|l|}
+\hline
+\multicolumn{2}{|l|}{\multirow{2}{*}{\begin{tabular}[c]{@{}l@{}}Program \\ name\end{tabular}}} & \multicolumn{2}{l|}{Energy saving \%} & \multicolumn{2}{l|}{Perf. degradation \%} & \multicolumn{2}{l|}{Distance} \\ \cline{3-8}
+\multicolumn{2}{|l|}{} & EDP & MaxDist & EDP & MaxDist & EDP & MaxDist \\ \hline
+\multicolumn{2}{|l|}{CG} & 27.58 & 31.25 & 5.82 & 7.12 & 21.76 & 24.13 \\ \hline
+\multicolumn{2}{|l|}{MG} & 29.49 & 33.78 & 3.74 & 6.41 & 25.75 & 27.37 \\ \hline
+\multicolumn{2}{|l|}{LU} & 19.55 & 28.33 & 0.0 & 0.01 & 19.55 & 28.22 \\ \hline
+\multicolumn{2}{|l|}{EP} & 28.40 & 27.04 & 4.29 & 0.49 & 24.11 & 26.55 \\ \hline
+\multicolumn{2}{|l|}{BT} & 27.68 & 32.32 & 6.45 & 7.87 & 21.23 & 24.43 \\ \hline
+\multicolumn{2}{|l|}{SP} & 20.52 & 24.73 & 5.21 & 2.78 & 15.31 & 21.95 \\ \hline
+\multicolumn{2}{|l|}{FT} & 27.03 & 31.02 & 2.75 & 2.54 & 24.28 & 28.48 \\ \hline
+
+\end{tabular}
+\label{table:compare_EDP}
+\end{table}
+
+
+\begin{table}[htb]
+ \caption{Comparing the proposed algorithm}
+ % title of Table
+ \centering
+ \begin{tabular}{|*{4}{l|}}
+ \hline
+ Program & Energy & Performance & Distance\% \\
+ name & saving\% & degradation\% & \\
+ \hline
+ CG &13.31 &22.34 &10.89 \\
+ \hline
+ MG &14.55 &71.39 &6.29 \\
+ \hline
+ EP &44.4 &0.0 &44.42 \\
+ \hline
+ LU &-4.79 &-88.58 &10.12 \\
+ \hline
+ BT &16.76 &22.33 &15.07 \\
+ \hline
+ SP &20.52 &-46.64 &43.37 \\
+ \hline
+ FT &14.76 &-7.64 &17.3 \\
+\hline
+ \end{tabular}
+ \label{table:compare_EDP}
+\end{table}
+
+\begin{table}[htb]
+ \caption{Comparing the proposed algorithm}
+ % title of Table
+ \centering
+ \begin{tabular}{|*{4}{l|}}
+ \hline
+ Program & Energy & Performance & Distance\% \\
+ name & saving\% & degradation\% & \\
+ \hline
+ CG &3.67 &1.3 &2.37 \\
+ \hline
+ MG &4.29 &2.67 &1.62 \\
+ \hline
+ EP &8.68 &0.01 &8.67 \\
+ \hline
+ LU &-1.36 &-3.8 &2.44 \\
+ \hline
+ BT &4.64 &1.44 &3.2 \\
+ \hline
+ SP &4.21 &-2.43 &6.64 \\
+ \hline
+ FT &3.99 &-0.21 &4.2
+ \\
+\hline
+ \end{tabular}
+ \label{table:compare_EDP}
+\end{table}
+\begin{figure}[t]
+ \centering
+ \includegraphics[scale=0.5]{fig/compare_EDP.pdf}
+ \caption{Tradeoff comparison for NAS benchmarks class C}
+ \label{fig:compare_EDP}
+\end{figure}
+
