+\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\%.}
+
+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}[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{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}
+
