adding comparison section

diff --git a/Heter_paper.tex b/Heter_paper.tex
index f34524c8eea7c8969751c9fffa2de636c3550266..d31891279930b9743c2e58c7b367fefb4c3a4c37 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -8,7 +8,7 @@
 \usepackage{algorithm}
 \usepackage{subfig}
 \usepackage{amsmath}
-
+\usepackage{multirow}
 \usepackage{url}
 \DeclareUrlCommand\email{\urlstyle{same}}
 
@@ -207,7 +207,7 @@ task which have the highest computation time and no slack time.
   
  \begin{figure}[t]
   \centering
-   \includegraphics[scale=0.6]{fig/commtasks}
+   \includegraphics[scale=0.5]{fig/commtasks}
   \caption{Parallel tasks on a heterogeneous platform}
   \label{fig:heter}
 \end{figure}
@@ -266,7 +266,7 @@ by the number of iterations of that application.
 
 This prediction model is developed from the model for predicting the execution time of 
 message passing distributed applications for homogeneous architectures~\cite{Our_first_paper}. 
-The execution time prediction model is used in the method for optimizing both 
+The execution time prediction model is uSpiliopoulossed in the method for optimizing both 
 energy consumption and performance of iterative methods, which is presented in the 
 following sections.
 
@@ -670,16 +670,16 @@ Finally, These nodes were connected via an ethernet network with 1 Gbit/s bandwi
                   &           & GHz      & GHz          &GHz             &              &       \\
     \hline
     1             &40         & 2.5      & 1.2          & 0.1            & 20~w         &4~w    \\
-                  &           &          &              &                &              &  \\
+         
     \hline
     2             &50         & 2.66     & 1.6          & 0.133          & 25~w         &5~w    \\
-                  &           &          &              &                &              &  \\
+                  
     \hline
     3             &60         & 2.9      & 1.2          & 0.1            & 30~w         &6~w    \\
-                  &           &          &              &                &              &  \\
+                  
     \hline
     4             &70         & 3.4      & 1.6          & 0.133          & 35~w         &7~w    \\
-                  &           &          &              &                &              &  \\
+                  
     \hline
   \end{tabular}
   \label{table:platform}
@@ -708,7 +708,7 @@ The other benchmarks such as BT and SP should be executed on $1, 4, 9, 16, 36, 6
   \centering
   \begin{tabular}{|*{7}{l|}}
     \hline
-    Method     & Execution     & Energy         & Energy      & Performance        & Distance      \\
+    Program     & Execution     & Energy         & Energy      & Performance        & Distance      \\
     name       & time/s        & consumption/J  & saving\%    & degradation\%      &               \\
     \hline
     CG         &  64.64        & 3560.39        &34.16        &6.72               &27.44       \\
@@ -735,7 +735,7 @@ The other benchmarks such as BT and SP should be executed on $1, 4, 9, 16, 36, 6
   \centering
   \begin{tabular}{|*{7}{l|}}
     \hline
-    Method     & Execution     & Energy         & Energy      & Performance        & Distance      \\
+    Program    & Execution     & Energy         & Energy      & Performance        & Distance      \\
     name       & time/s        & consumption/J  & saving\%    & degradation\%      &               \\
     \hline
     CG         &36.11             &3263.49             &31.25        &7.12                    &24.13     \\
@@ -762,7 +762,7 @@ The other benchmarks such as BT and SP should be executed on $1, 4, 9, 16, 36, 6
   \centering
   \begin{tabular}{|*{7}{l|}}
     \hline
-    Method     & Execution     & Energy         & Energy      & Performance        & Distance      \\
+    Program     & Execution     & Energy         & Energy      & Performance        & Distance      \\
     name       & time/s        & consumption/J  & saving\%    & degradation\%      &               \\
     \hline
     CG         &31.74         &4373.90         &26.29        &9.57                    &16.72          \\
@@ -789,7 +789,7 @@ The other benchmarks such as BT and SP should be executed on $1, 4, 9, 16, 36, 6
   \centering
   \begin{tabular}{|*{7}{l|}}
     \hline
-    Method     & Execution     & Energy         & Energy      & Performance        & Distance      \\
+    Program    & Execution     & Energy         & Energy      & Performance        & Distance      \\
     name       & time/s        & consumption/J  & saving\%    & degradation\%      &               \\
     \hline
     CG         &32.35         &6704.21         &16.15        &5.30                    &10.85           \\
@@ -816,7 +816,7 @@ The other benchmarks such as BT and SP should be executed on $1, 4, 9, 16, 36, 6
   \centering
   \begin{tabular}{|*{7}{l|}}
     \hline
-    Method     & Execution     & Energy         & Energy      & Performance        & Distance      \\
+    Program    & Execution     & Energy         & Energy      & Performance        & Distance      \\
     name       & time/s        & consumption/J  & saving\%    & degradation\%      &               \\
     \hline
     CG         &46.65         &17521.83            &8.13             &1.68                    &6.45           \\
@@ -844,7 +844,7 @@ The other benchmarks such as BT and SP should be executed on $1, 4, 9, 16, 36, 6
   \centering
   \begin{tabular}{|*{7}{l|}}
     \hline
-    Method     & Execution     & Energy         & Energy      & Performance        & Distance     \\
+    Program    & Execution     & Energy         & Energy      & Performance        & Distance     \\
     name       & time/s        & consumption/J  & saving\%    & degradation\%      &              \\
     \hline
     CG         &56.92         &41163.36        &4.00         &1.10                    &2.90          \\
@@ -964,7 +964,7 @@ results in less energy saving but less performance degradation.
   \centering
   \begin{tabular}{|*{6}{l|}}
     \hline
-    Method     & Energy          & Energy      & Performance        & Distance     \\
+    Program    & Energy          & Energy      & Performance        & Distance     \\
     name       & consumption/J   & saving\%    & degradation\%      &              \\
     \hline
     CG         &4144.21          &22.42        &7.72                &14.70         \\
@@ -993,7 +993,7 @@ results in less energy saving but less performance degradation.
   \centering
   \begin{tabular}{|*{6}{l|}}
     \hline
-    Method     & Energy          & Energy      & Performance        & Distance     \\
+    Program    & Energy          & Energy      & Performance        & Distance     \\
     name       & consumption/J   & saving\%    & degradation\%      &              \\
     \hline
     CG         &2812.38                 &36.36        &6.80                &29.56         \\
@@ -1017,11 +1017,11 @@ results in less energy saving but less performance degradation.
 
 \begin{figure}
   \centering
-  \subfloat[Comparison the average of the results on 8 nodes]{%
-    \includegraphics[width=.33\textwidth]{fig/sen_comp}\label{fig:sen_comp}}%
+  \subfloat[Comparison  of the results on 8 nodes]{%
+    \includegraphics[width=.30\textwidth]{fig/sen_comp}\label{fig:sen_comp}}%
 
   \subfloat[Comparison the selected frequency scaling factors of MG benchmark class C running on 8 nodes]{%
-    \includegraphics[width=.33\textwidth]{fig/three_scenarios}\label{fig:scales_comp}}
+    \includegraphics[width=.34\textwidth]{fig/three_scenarios}\label{fig:scales_comp}}
   \label{fig:comp}
   \caption{The comparison of the three power scenarios}
 \end{figure}  
@@ -1029,6 +1029,59 @@ results in less energy saving but less performance degradation.
 
 
 
+\subsection{The comparison of the proposed scaling algorithm }
+\label{sec.compare_EDP}
+
+In this section, we compare our scaling  factors selection algorithm
+with Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}. 
+They developed an online frequency selecting algorithm running over multicore architecture. 
+The algorithm predicted both the energy and performance during the runtime of the program, then 
+selecting the frequencies that minimized the energy and delay products (EDP), $EDP=Enegry * Delay$. 
+To be able to compare with this algorithm, we used our energy and execution time models in prediction process,
+equations (\ref{eq:energy}) and  (\ref{eq:fnew}). Also their algorithm is adapted to taking into account 
+the heterogeneous platform to starts selecting the 
+initial frequencies using the equation (\ref{eq:Fint}). The algorithm built to test all possible frequencies as 
+a brute-force search algorithm. 
+
+The comparison results of running NAS benchmarks class C on 8 or 9 nodes are 
+presented in table \ref{table:compare_EDP}. The results show that our algorithm has a biggest energy saving percentage, 
+on average it has 29.76\% and thier algorithm has 25.75\%,
+while the average of performance degradation percentage is approximately the same, the average for our algorithm is 
+equal to 3.89\% and for their algorithm is equal to 4.03\%. In general, our algorithm outperforms 
+Spiliopoulos et al. algorithm in term of energy and performance tradeoff see figure (\ref{fig:compare_EDP}). 
+This because our algorithm maximized the difference (the distance) between the energy saving and the performance degradation 
+comparing to their EDP optimization function. It is also keeps the frequency of the slowest node without change 
+that gave some enhancements to the energy and performance tradeoff.
+
+
+\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{figure}[t]
+  \centering
+   \includegraphics[scale=0.6]{fig/compare_EDP.pdf}
+  \caption{Tradeoff comparison for NAS benchmarks class C}
+  \label{fig:compare_EDP}
+\end{figure}
+
 
 \section{Conclusion}
 \label{sec.concl} 
@@ -1044,6 +1097,10 @@ known in advance and depends on the global convergence of the iterative system.
 
 \section*{Acknowledgment}
 
+This work has been partially supported by the Labex
+ACTION project (contract “ANR-11-LABX-01-01”). As a PhD student,
+Mr. Ahmed Fanfakh, would like to thank the University of
+Babylon (Iraq) for supporting his work.
 
 
 % trigger a \newpage just before the given reference

diff --git a/fig/compare_EDP.pdf b/fig/compare_EDP.pdf
new file mode 100644 (file)
index 0000000..1aaef32
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diff --git a/fig/sen_comp.pdf b/fig/sen_comp.pdf
index 7b1cf7042e53e287fa63bedb398dad03a6edfb8e..5d3e407bdc71dbd7742ec6b28dbe3ee26ea32509 100644 (file)
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diff --git a/fig/three_scenarios.pdf b/fig/three_scenarios.pdf
index f24e443a2ef7f0e4c8be5408a945bca434939389..4e2a400873dd5b3d4306ac1e0be1d80faad69869 100644 (file)
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diff --git a/my_reference.bib b/my_reference.bib
index 929e65c6ffad28b97e2f7167791d5fbc7e606270..5ceb5d64a2642bccda1d8ccea076a5d7123a43a8 100644 (file)
--- a/my_reference.bib
+++ b/my_reference.bib
@@ -743,7 +743,7 @@ author = {Lizhe Wang and Samee U. Khan and Dan Chen and Joanna Kołodziej and Ra
 
 @INPROCEEDINGS{Spiliopoulos_Green.governors.Adaptive.DVFS, 
 author={Spiliopoulos, V. and Kaxiras, S. and Keramidas, G.}, 
-booktitle={Green Computing Conference and Workshops (IGCC), 2011 International}, 
+booktitle={International Green Computing Conference and Workshops (IGCC)}, 
 title={Green governors: A framework for Continuously Adaptive DVFS}, 
 year={2011}, 
 month={July},