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+\documentclass[conference]{IEEEtran}
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\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\small\textbf{AG:} #2}}
\begin{document}
\title{Optimal Dynamic Frequency Scaling for Energy-Performance of Parallel MPI Programs}
-\author{A. Badri \and J.-C. Charr \and R. Couturier \and A. Giersch}
+
+\author{%
+ \IEEEauthorblockN{%
+ Ahmed Badri,
+ Jean-Claude Charr,
+ Raphaël Couturier and
+ Arnaud Giersch
+ }
+ \IEEEauthorblockA{%
+ FEMTO-ST Institute\\
+ University of Franche-Comté
+ }
+}
+
\maketitle
\AG{``Optimal'' is a bit pretentious in the title}
executed on this model can be either synchronous or asynchronous. In this paper
we consider execution of the synchronous tasks on distributed homogeneous
platform. These tasks can exchange the data via synchronous memory passing.
-\begin{figure}[h]
+\begin{figure*}[t]
\centering
\subfloat[Synch. Imbalanced Communications]{\includegraphics[scale=0.67]{synch_tasks}\label{fig:h1}}
\subfloat[Synch. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
\caption{Parallel Tasks on Homogeneous Platform}
\label{fig:homo}
-\end{figure}
+\end{figure*}
Therefore, the execution time of a task consists of the computation time and the
communication time. Moreover, the synchronous communications between tasks can
lead to idle time while tasks wait at the synchronous point for others tasks to
time values. These scaling factors are computed by dividing the maximum
frequency by the new one see EQ~(\ref{eq:s}). In all tests, we use the simulator
SimGrid/SMPI v3.10 to run the NAS programs.
-\begin{figure}[width=\textwidth,height=\textheight,keepaspectratio]
+\begin{figure*}[t]
\centering
- \includegraphics[scale=0.60]{cg_per.eps}
- \includegraphics[scale=0.60]{mg_pre.eps}
- \includegraphics[scale=0.60]{bt_pre.eps}
- \includegraphics[scale=0.60]{lu_pre.eps}
+ \includegraphics[width=.4\textwidth]{cg_per.eps}\qquad%
+ \includegraphics[width=.4\textwidth]{mg_pre.eps}
+ \includegraphics[width=.4\textwidth]{bt_pre.eps}\qquad%
+ \includegraphics[width=.4\textwidth]{lu_pre.eps}
\caption{Fitting Predicted to Real Execution Time}
\label{fig:pred}
-\end{figure}
+\end{figure*}
%see Figure~\ref{fig:pred}
In our cluster there are 18 available frequency states for each processor from
2.5 GHz to 800 MHz, there is 100 MHz difference between two successive
For solving this problem, we normalize the energy by calculating the ratio
between the consumed energy with scaled frequency and the consumed energy
without scaled frequency :
-\begin{equation}
+\begin{multline}
\label{eq:enorm}
- E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}}
- = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
+ E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}}\\
+ {} = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
\left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
P_{static} \cdot T_1 \cdot S_i \cdot N }{
P_{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
P_{static} \cdot T_1 \cdot N }
-\end{equation}
+\end{multline}
\AG{Use \texttt{\textbackslash{}text\{xxx\}} or
\texttt{\textbackslash{}textit\{xxx\}} for all subscripted words in equations
(e.g. \mbox{\texttt{E\_\{\textbackslash{}text\{Norm\}\}}}).
= \frac{T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
T_{\textit{Max Comm Old}}}
\end{equation}
-\begin{figure}
+\begin{figure*}
\centering
- \subfloat[Converted Relation.]{\includegraphics[scale=0.70]{file.eps}\label{fig:r1}}
- \subfloat[Real Relation.]{\includegraphics[scale=0.70]{file3.eps}\label{fig:r2}}
+ \subfloat[Converted Relation.]{%
+ \includegraphics[width=.4\textwidth]{file.eps}\label{fig:r1}}%
+ \qquad%
+ \subfloat[Real Relation.]{%
+ \includegraphics[width=.4\textwidth]{file3.eps}\label{fig:r2}}
\label{fig:rel}
\caption{The Energy and Performance Relation}
-\end{figure}
+\end{figure*}
Then, we can modelize our objective function as finding the maximum distance
between the energy curve EQ~(\ref{eq:enorm}) and the inverse of performance
curve EQ~(\ref{eq:pnorm_en}) over all available scaling factors. This represent
factors results for each program on class C. These factors give the maximum
energy saving percent and the minimum performance degradation percent in the
same time over all available scales.
-\begin{figure}[width=\textwidth,height=\textheight,keepaspectratio]
+\begin{figure*}
\centering
- \includegraphics[scale=0.47]{ep.eps}
- \includegraphics[scale=0.47]{cg.eps}
- \includegraphics[scale=0.47]{sp.eps}
- \includegraphics[scale=0.47]{lu.eps}
- \includegraphics[scale=0.47]{bt.eps}
- \includegraphics[scale=0.47]{ft.eps}
+ \includegraphics[width=.33\textwidth]{ep.eps}\hfill%
+ \includegraphics[width=.33\textwidth]{cg.eps}\hfill%
+ \includegraphics[width=.33\textwidth]{sp.eps}
+ \includegraphics[width=.33\textwidth]{lu.eps}\hfill%
+ \includegraphics[width=.33\textwidth]{bt.eps}\hfill%
+ \includegraphics[width=.33\textwidth]{ft.eps}
\caption{Optimal scaling factors for The NAS MPI Programs}
\label{fig:nas}
-\end{figure}
-\begin{table}[width=\textwidth,height=\textheight,keepaspectratio]
+\end{figure*}
+\begin{table}
\caption{Optimal Scaling Factors Results}
% title of Table
\centering
paper. While the negative trade offs refers to improving energy saving (or may
be the performance) while degrading the performance (or may be the energy) more
than the first.
-\begin{figure}[width=\textwidth,height=\textheight,keepaspectratio]
+\begin{figure*}
\centering
- \includegraphics[scale=0.60]{compare_class_A.pdf}
- \includegraphics[scale=0.60]{compare_class_B.pdf}
- \includegraphics[scale=0.60]{compare_class_c.pdf}
- % use scale 35 for all to be in the same line
+ \includegraphics[width=.33\textwidth]{compare_class_A.pdf}\hfill%
+ \includegraphics[width=.33\textwidth]{compare_class_B.pdf}\hfill%
+ \includegraphics[width=.33\textwidth]{compare_class_c.pdf}
\caption{Comparing Our EPSA with Rauber's Methods}
\label{fig:compare}
-\end{figure}
+\end{figure*}
\section{Conclusion}
\label{sec.conc}
Computations have been performed on the supercomputer facilities of the
Mésocentre de calcul de Franche-Comté.
-\bibliographystyle{plain}
-\bibliography{my_reference}
+\bibliographystyle{IEEEtran}
+\bibliography{IEEEabrv,my_reference}
\end{document}
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