-\documentclass[12pt]{article}
-%\documentclass[12pt,twocolumn]{article}
+\documentclass[conference]{IEEEtran}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
% \usepackage{secdot}
%\usepackage[font={footnotesize,bt}]{caption}
%\usepackage[font=scriptsize,labelfont=bf]{caption}
-\usepackage{lmodern}
-
-\usepackage{todonotes}
-\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\small\textbf{AG:} #2}}
+\usepackage[textsize=footnotesize]{todonotes}
+\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\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}
+\AG{``Optimal'' is a bit pretentious in the title.\\
+ Complete affiliation, add an email address, etc.}
\begin{abstract}
- \AG{FIXME}
+ \AG{complete the abstract\dots}
\end{abstract}
\section{Introduction}
+\label{sec.intro}
The need for computing power is still increasing and it is not expected to slow
down in the coming years. To satisfy this demand, researchers and supercomputers
constructors have been regularly increasing the number of computing cores in
-supercomputers (for example in November 2013, according to the top 500
+supercomputers (for example in November 2013, according to the TOP500
list~\cite{43}, the Tianhe-2 was the fastest supercomputer. It has more than 3
millions of cores and delivers more than 33 Tflop/s while consuming 17808
kW). This large increase in number of computing cores has led to large energy
benchmarks (NPB v3.3) developed by NASA~\cite{44}. Our experiments are executed
using the simulator SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183}
over an homogeneous distributed memory architecture. Furthermore, we compare the
-proposed algorithm with Rauber's methods. The comparison's results show that our
+proposed algorithm with Rauber's methods.
+\AG{Add citation for Rauber's methods. Moreover, Rauber was not alone to to this work (use ``Rauber et al.'', or ``Rauber and Gudula'', or \dots)}
+The comparison's results show that our
algorithm gives better energy-time trade off.
+%
+\AG{Correctly reword the following}%
+In Section~\ref{sec.relwork} we present works from other
+authors. Then, in Sections~\ref{sec.ptasks} and~\ref{sec.energy}, we
+introduce our model. [\dots] Finally, we conclude in
+Section~\ref{sec.concl}.
\section{Related Works}
+\label{sec.relwork}
+
+\AG{Consider introducing the models (sec.~\ref{sec.ptasks},
+ maybe~\ref{sec.energy}) before related works}
In the this section some heuristics, to compute the scaling factor, are
presented and classified in two parts : offline and online methods.
\end{enumerate}
\section{Parallel Tasks Execution on Homogeneous Platform}
+\label{sec.ptasks}
A homogeneous cluster consists of identical nodes in terms of the hardware and
the software. Each node has its own memory and at least one processor which can
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
where $T_i$ is the execution time of process $i$.
\section{Energy Model for Homogeneous Platform}
+\label{sec.energy}
The energy consumption by the processor consists of two powers metric: the
dynamic and the static power. This general power formulation is used by many
\end{equation}
\section{Performance Evaluation of MPI Programs}
+\label{sec.mpip}
The performance (execution time) of the parallel MPI applications are depends on
the time of the slowest task as in figure~(\ref{fig:homo}). Normally the
investigation study for the EQ~(\ref{eq:tnew}).
\section{Performance Prediction Verification}
+\label{sec.verif}
In this section we evaluate the precision of our performance prediction methods
on the NAS benchmark. We use the EQ~(\ref{eq:tnew}) that predicts the execution
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.
-\AG{Fig.~\ref{fig:pred} is hard to read when printed in black and white,
- especially the ``Normalize Real Perf.'' curve.}
-\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
figure~(\ref{fig:pred}).
\section{Performance to Energy Competition}
+\label{sec.compet}
+
This section demonstrates our approach for choosing the optimal scaling
factor. This factor gives maximum energy reduction taking into account the
execution time for both computation and communication times . The relation
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_{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=.33\textwidth]{file.eps}\label{fig:r1}}%
+ \qquad%
+ \subfloat[Real Relation.]{%
+ \includegraphics[width=.33\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
reasons that mentioned before.
\section{Optimal Scaling Factor for Performance and Energy}
+\label{sec.optim}
In the previous section we described the objective function that satisfy our
goal in discovering optimal scaling factor for both performance and energy at
the same time. Therefore, we develop an energy to performance scaling algorithm
(EPSA). This algorithm is simple and has a direct way to calculate the optimal
scaling factor for both energy and performance at the same time.
-\begin{algorithm}[t]
+\begin{algorithm}[tp]
\caption{EPSA}
\label{EPSA}
\begin{algorithmic}[1]
MPI program calls the EPSA algorithm to choose the new frequency using the
optimal scaling factor. Then the program set the new frequency to the
system. The algorithm is called just one time during the execution of the
-program. The following example shows where and when the EPSA algorithm is called
-in the MPI program :
-\begin{minipage}{\textwidth}
-\AG{Use the same format as for Algorithm~\ref{EPSA}}
-\begin{lstlisting}[frame=tb]
-FOR J:=1 to Some_iterations Do
- -Computations Section.
- -Communications Section.
- IF (J==1) THEN
- -Gather all times of computation and communication
- from each node.
- -Call EPSA with these times.
- -Calculate the new frequency from optimal scale.
- -Set the new frequency to the system.
- ENDIF
-ENDFOR
-\end{lstlisting}
-\end{minipage}
+program. The DVFS algorithm~(\ref{dvfs}) shows where and when the EPSA algorithm is called
+in the MPI program.
+%\begin{minipage}{\textwidth}
+%\AG{Use the same format as for Algorithm~\ref{EPSA}}
+
+\begin{algorithm}[tp]
+ \caption{DVFS}
+ \label{dvfs}
+ \begin{algorithmic}
+ \For {$J:=1$ to $Some-Iterations \; $}
+ \State -Computations Section.
+ \State -Communications Section.
+ \If {$(J==1)$}
+ \State -Gather all times of computation and\par
+ \State communication from each node.
+ \State -Call EPSA with these times.
+ \State -Calculate the new frequency from optimal scale.
+ \State -Set the new frequency to the system.
+ \EndIf
+\EndFor
+\end{algorithmic}
+\end{algorithm}
+
After obtaining the optimal scale factor from the EPSA algorithm. The program
calculates the new frequency $F_i$ for each task proportionally to its time
value $T_i$. By substitution of the EQ~(\ref{eq:s}) in the EQ~(\ref{eq:si}), we
the frequency according to the nodes workloads.
\section{Experimental Results}
+\label{sec.expe}
The proposed EPSA algorithm was applied to seven MPI programs of the NAS
benchmarks (EP, CG, MG, FT, BT, LU and SP). We work on three classes (A, B and
table~(\ref{table:platform}). Each node in the cluster has 18 frequency values
from 2.5 GHz to 800 MHz with 100 MHz difference between each two successive
frequencies.
-\begin{table}[ht]
+\begin{table}[htb]
\caption{Platform File Parameters}
% title of Table
\centering
- \AG{Use e.g. $5\times 10^{-7}$ instead of 5E-7}
\begin{tabular}{ | l | l | l |l | l |l |l | p{2cm} |}
\hline
Max & Min & Backbone & Backbone&Link &Link& Sharing \\
Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy \\ \hline
- 2.5 &800 & 2.25 GBps &5E-7 s & 1 GBps & 5E-5 s&Full \\
+ 2.5 &800 & 2.25 GBps &$5\times 10^{-7} s$& 1 GBps & $5\times 10^{-5}$ s&Full \\
GHz& MHz& & & & &Duplex \\\hline
\end{tabular}
\label{table:platform}
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*}[t]
\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}[htb]
\caption{Optimal Scaling Factors Results}
% title of Table
\centering
\hline
Program & Optimal & Energy & Performance&Energy-Perf.\\
Name & Scaling Factor& Saving \%&Degradation \% &Distance \\ \hline
- CG & 1.56 &39.23 & 14.88 & 24.35\\ \hline
- MG & 1.47 &34.97&21.7& 13.27 \\ \hline
+ CG & 1.56 &39.23&14.88 &24.35\\ \hline
+ MG & 1.47 &34.97&21.70 &13.27 \\ \hline
EP & 1.04 &22.14&20.73 &1.41\\ \hline
- LU & 1.388 &35.83&22.49 &13.34\\ \hline
- BT & 1.315 &29.6&21.28 &8.32\\ \hline
- SP & 1.388 &33.48 &21.36&12.12\\ \hline
- FT & 1.47 &34.72 &19&15.72\\ \hline
+ LU & 1.38 &35.83&22.49 &13.34\\ \hline
+ BT & 1.31 &29.60&21.28 &8.32\\ \hline
+ SP & 1.38 &33.48&21.36 &12.12\\ \hline
+ FT & 1.47 &34.72&19.00 &15.72\\ \hline
\end{tabular}
\label{table:factors results}
% is used to refer this table in the text
EPSA to selects smaller scaling factor values (inducing smaller energy savings).
\section{Comparing Results}
+\label{sec.compare}
In this section, we compare our EPSA algorithm results with Rauber's
methods~\cite{3}. He had two scenarios, the first is to reduce energy to optimal
Class A},\ref{table:compare Class B},\ref{table:compare Class C}). These
tables show the results of our EPSA and Rauber's two scenarios for all the NAS
benchmarks programs for classes A,B and C.
-\begin{table}[ht]
+\begin{table*}[p]
\caption{Comparing Results for The NAS Class A}
% title of Table
\centering
- \begin{tabular}{ | l | l | l |l | l |l| }
+ \begin{tabular}{ | l | l | l |l | l | l| }
\hline
Method&Program&Factor& Energy& Performance &Energy-Perf.\\
name &name&value& Saving \%&Degradation \% &Distance
\\ \hline
% \rowcolor[gray]{0.85}
EPSA&CG & 1.56 &37.02 & 13.88 & 23.14\\ \hline
- $Rauber_{E-P}$&CG &2.14 &42.77 & 25.27 & 17.5\\ \hline
+ $Rauber_{E-P}$&CG &2.14 &42.77 & 25.27 & 17.50\\ \hline
$Rauber_{E}$&CG &2.14 &42.77&26.46&16.31\\ \hline
EPSA&MG & 1.47 &27.66&16.82&10.84\\ \hline
$Rauber_{E-P}$&MG &2.14&34.45&31.84&2.61\\ \hline
- $Rauber_{E}$&MG &2.14&34.48&33.65&0.8 \\ \hline
+ $Rauber_{E}$&MG &2.14&34.48&33.65&0.80 \\ \hline
EPSA&EP &1.19 &25.32&20.79&4.53\\ \hline
$Rauber_{E-P}$&EP&2.05&41.45&55.67&-14.22\\ \hline
- $Rauber_{E}$&EP&2.05&42.09&57.59&-15.5\\ \hline
+ $Rauber_{E}$&EP&2.05&42.09&57.59&-15.50\\ \hline
EPSA&LU&1.56& 39.55 &19.38& 20.17\\ \hline
- $Rauber_{E-P}$&LU&2.14&45.62&27&18.62 \\ \hline
+ $Rauber_{E-P}$&LU&2.14&45.62&27.00&18.62 \\ \hline
$Rauber_{E}$&LU&2.14&45.66&33.01&12.65\\ \hline
- EPSA&BT&1.315& 29.6&20.53&9.07 \\ \hline
- $Rauber_{E-P}$&BT&2.1&45.53&49.63&-4.1\\ \hline
- $Rauber_{E}$&BT&2.1&43.93&52.86&-8.93\\ \hline
+ EPSA&BT&1.31& 29.60&20.53&9.07 \\ \hline
+ $Rauber_{E-P}$&BT&2.10&45.53&49.63&-4.10\\ \hline
+ $Rauber_{E}$&BT&2.10&43.93&52.86&-8.93\\ \hline
- EPSA&SP&1.388& 33.51&15.65&17.86 \\ \hline
- $Rauber_{E-P}$&SP&2.11&45.62&42.52&3.1\\ \hline
+ EPSA&SP&1.38& 33.51&15.65&17.86 \\ \hline
+ $Rauber_{E-P}$&SP&2.11&45.62&42.52&3.10\\ \hline
$Rauber_{E}$&SP&2.11&45.78&43.09&2.69\\ \hline
- EPSA&FT&1.25& 25&10.8&14.2 \\ \hline
- $Rauber_{E-P}$&FT&2.1&39.29&34.3&4.99 \\ \hline
- $Rauber_{E}$&FT&2.1&37.56&38.21&-0.65\\ \hline
+ EPSA&FT&1.25&25.00&10.80&14.20 \\ \hline
+ $Rauber_{E-P}$&FT&2.10&39.29&34.30&4.99 \\ \hline
+ $Rauber_{E}$&FT&2.10&37.56&38.21&-0.65\\ \hline
\end{tabular}
\label{table:compare Class A}
% is used to refer this table in the text
-\end{table}
-\begin{table}[ht]
+\end{table*}
+\begin{table*}[p]
\caption{Comparing Results for The NAS Class B}
% title of Table
\centering
name &name&value& Saving \%&Degradation \% &Distance
\\ \hline
% \rowcolor[gray]{0.85}
- EPSA&CG & 1.66 &39.23&16.63&22.6 \\ \hline
- $Rauber_{E-P}$&CG &2.15 &45.34&27.6&17.74\\ \hline
+ EPSA&CG & 1.66 &39.23&16.63&22.60 \\ \hline
+ $Rauber_{E-P}$&CG &2.15 &45.34&27.60&17.74\\ \hline
$Rauber_{E}$&CG &2.15 &45.34&28.88&16.46\\ \hline
EPSA&MG & 1.47 &34.98&18.35&16.63\\ \hline
$Rauber_{E}$&MG &2.14&43.56&37.07&6.49 \\ \hline
EPSA&EP &1.08 &20.29&17.15&3.14 \\ \hline
- $Rauber_{E-P}$&EP&2&42.38&56.88&-14.5\\ \hline
- $Rauber_{E}$&EP&2&39.73&59.94&-20.21\\ \hline
+ $Rauber_{E-P}$&EP&2.00&42.38&56.88&-14.50\\ \hline
+ $Rauber_{E}$&EP&2.00&39.73&59.94&-20.21\\ \hline
EPSA&LU&1.47&38.57&21.34&17.23 \\ \hline
- $Rauber_{E-P}$&LU&2.1&43.62&36.51&7.11 \\ \hline
- $Rauber_{E}$&LU&2.1&43.61&38.54&5.07 \\ \hline
+ $Rauber_{E-P}$&LU&2.10&43.62&36.51&7.11 \\ \hline
+ $Rauber_{E}$&LU&2.10&43.61&38.54&5.07 \\ \hline
- EPSA&BT&1.315& 29.59&20.88&8.71\\ \hline
- $Rauber_{E-P}$&BT&2.1&44.53&53.05&-8.52\\ \hline
- $Rauber_{E}$&BT&2.1&42.93&52.806&-9.876\\ \hline
+ EPSA&BT&1.31& 29.59&20.88&8.71\\ \hline
+ $Rauber_{E-P}$&BT&2.10&44.53&53.05&-8.52\\ \hline
+ $Rauber_{E}$&BT&2.10&42.93&52.80&-9.87\\ \hline
- EPSA&SP&1.388&33.44&19.24&14.2 \\ \hline
- $Rauber_{E-P}$&SP&2.15&45.69&43.2&2.49\\ \hline
+ EPSA&SP&1.38&33.44&19.24&14.20 \\ \hline
+ $Rauber_{E-P}$&SP&2.15&45.69&43.20&2.49\\ \hline
$Rauber_{E}$&SP&2.15&45.41&44.47&0.94\\ \hline
- EPSA&FT&1.388&34.4&14.57&19.83 \\ \hline
+ EPSA&FT&1.38&34.40&14.57&19.83 \\ \hline
$Rauber_{E-P}$&FT&2.13&42.98&37.35&5.63 \\ \hline
- $Rauber_{E}$&FT&2.13&43.04&37.9&5.14\\ \hline
+ $Rauber_{E}$&FT&2.13&43.04&37.90&5.14\\ \hline
\end{tabular}
\label{table:compare Class B}
% is used to refer this table in the text
-\end{table}
+\end{table*}
-\begin{table}[ht]
+\begin{table*}[p]
\caption{Comparing Results for The NAS Class C}
% title of Table
\centering
% \rowcolor[gray]{0.85}
EPSA&CG & 1.56 &39.23&14.88&24.35 \\ \hline
$Rauber_{E-P}$&CG &2.15 &45.36&25.89&19.47\\ \hline
- $Rauber_{E}$&CG &2.15 &45.36&26.7&18.66\\ \hline
+ $Rauber_{E}$&CG &2.15 &45.36&26.70&18.66\\ \hline
- EPSA&MG & 1.47 &34.97&21.697&13.273\\ \hline
- $Rauber_{E-P}$&MG &2.15&43.65&40.45&3.2 \\ \hline
+ EPSA&MG & 1.47 &34.97&21.69&13.27\\ \hline
+ $Rauber_{E-P}$&MG &2.15&43.65&40.45&3.20 \\ \hline
$Rauber_{E}$&MG &2.15&43.64&41.38&2.26 \\ \hline
EPSA&EP &1.04 &22.14&20.73&1.41 \\ \hline
- $Rauber_{E-P}$&EP&1.92&39.4&56.33&-16.93\\ \hline
- $Rauber_{E}$&EP&1.92&38.1&56.35&-18.25\\ \hline
+ $Rauber_{E-P}$&EP&1.92&39.40&56.33&-16.93\\ \hline
+ $Rauber_{E}$&EP&1.92&38.10&56.35&-18.25\\ \hline
- EPSA&LU&1.388&35.83&22.49&13.34 \\ \hline
- $Rauber_{E-P}$&LU&2.15&44.97&41&3.97 \\ \hline
- $Rauber_{E}$&LU&2.15&44.97&41.8&3.17 \\ \hline
+ EPSA&LU&1.38&35.83&22.49&13.34 \\ \hline
+ $Rauber_{E-P}$&LU&2.15&44.97&41.00&3.97 \\ \hline
+ $Rauber_{E}$&LU&2.15&44.97&41.80&3.17 \\ \hline
- EPSA&BT&1.315& 29.6&21.28&8.32\\ \hline
- $Rauber_{E-P}$&BT&2.13&45.6&49.84&-4.24\\ \hline
- $Rauber_{E}$&BT&2.13&44.9&55.16&-10.26\\ \hline
+ EPSA&BT&1.31& 29.60&21.28&8.32\\ \hline
+ $Rauber_{E-P}$&BT&2.13&45.60&49.84&-4.24\\ \hline
+ $Rauber_{E}$&BT&2.13&44.90&55.16&-10.26\\ \hline
- EPSA&SP&1.388&33.48&21.35&12.12\\ \hline
- $Rauber_{E-P}$&SP&2.1&45.69&43.6&2.09\\ \hline
- $Rauber_{E}$&SP&2.1&45.75&44.1&1.65\\ \hline
+ EPSA&SP&1.38&33.48&21.35&12.12\\ \hline
+ $Rauber_{E-P}$&SP&2.10&45.69&43.60&2.09\\ \hline
+ $Rauber_{E}$&SP&2.10&45.75&44.10&1.65\\ \hline
- EPSA&FT&1.47&34.72&19&15.72 \\ \hline
- $Rauber_{E-P}$&FT&2.04&39.4&37.1&2.3\\ \hline
- $Rauber_{E}$&FT&2.04&39.35&37.7&1.65\\ \hline
+ EPSA&FT&1.47&34.72&19.00&15.72 \\ \hline
+ $Rauber_{E-P}$&FT&2.04&39.40&37.10&2.30\\ \hline
+ $Rauber_{E}$&FT&2.04&39.35&37.70&1.65\\ \hline
\end{tabular}
\label{table:compare Class C}
% is used to refer this table in the text
-\end{table}
+\end{table*}
As shown in these tables our scaling factor is not optimal for energy saving
such as Rauber's scaling factor EQ~(\ref{eq:sopt}), but it is optimal for both
the energy and the performance simultaneously. Our EPSA optimal scaling factors
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}[t]
\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}
+ \includegraphics[width=.33\textwidth]{compare_class_B.pdf}
+ \includegraphics[width=.33\textwidth]{compare_class_c.pdf}
\caption{Comparing Our EPSA with Rauber's Methods}
\label{fig:compare}
\end{figure}
-\AG{\texttt{bibtex} gives many errors, please correct them}
-\bibliographystyle{plain}
-\bibliography{my_reference}
+\section{Conclusion}
+\label{sec.concl}
+
+\AG{the conclusion needs to be written\dots{} one day}
+
+\section*{Acknowledgment}
+
+\AG{Right?}
+Computations have been performed on the supercomputer facilities of the
+Mésocentre de calcul de Franche-Comté.
+
+\bibliographystyle{IEEEtran}
+\bibliography{IEEEabrv,my_reference}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
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-%%% ispell-local-dictionary: "american"
+%%%ispell-local-dictionary: "american"
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% LocalWords: Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
