More todos.

[mpi-energy.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 29f175b812587aec180d539e40edcaf71fa594b5..bfa1bc123373a5f472f6d8cc6a349e7fd2baba36 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -1,5 +1,4 @@
-\documentclass[12pt]{article}
-%\documentclass[12pt,twocolumn]{article}
+\documentclass[conference]{IEEEtran}

 
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
 
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}


@@ -15,29 +14,42 @@
 % \usepackage{secdot}
 %\usepackage[font={footnotesize,bt}]{caption}
 %\usepackage[font=scriptsize,labelfont=bf]{caption}
 % \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}
 
 \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
 
 \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}
 
 \begin{abstract}

-  \AG{FIXME}
+  \AG{complete the abstract\dots}

 \end{abstract}
 
 \section{Introduction}
 \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
 
 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
 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


@@ -72,10 +84,22 @@ this algorithm to seven MPI benchmarks. These MPI programs are the NAS parallel
 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
 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.
 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}
 
 \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.
 
 In the this section some heuristics, to compute the scaling factor, are
 presented and classified in two parts : offline and online methods.


@@ -132,6 +156,7 @@ paper.  However, the primary contributions of this paper are:
 \end{enumerate}
 
 \section{Parallel Tasks Execution on Homogeneous Platform}
 \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
 
 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


@@ -139,13 +164,13 @@ be a multi-core. The nodes are connected via a high bandwidth network. Tasks
 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.
 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}
   \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
 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


@@ -162,6 +187,7 @@ of the program is the execution time of the slowest task as :
 where $T_i$ is the execution time of process $i$.
 
 \section{Energy Model for Homogeneous Platform}
 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
 
 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


@@ -246,6 +272,7 @@ scaling factor as in EQ~(\ref{eq:sopt}).
 \end{equation}
 
 \section{Performance Evaluation of MPI Programs}
 \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
 
 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


@@ -285,6 +312,7 @@ method as we will show in the coming sections. In the next section we make an
 investigation study for the EQ~(\ref{eq:tnew}).
 
 \section{Performance Prediction Verification}
 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
 
 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


@@ -294,17 +322,15 @@ with all available scaling factors on 8 or 9 nodes to produce real 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.
 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
   \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}
   \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
 %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


@@ -317,6 +343,8 @@ example, we are present the execution times of the NAS benchmarks as in the
 figure~(\ref{fig:pred}).
 
 \section{Performance to Energy Competition}
 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
 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


@@ -327,15 +355,15 @@ is not straightforward. Moreover, they are not measured using the same metric.
 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 :
 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}
   \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 }
                \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\}\}}}).
 \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\}\}}}).


@@ -371,13 +399,16 @@ performance as follows :
                = \frac{T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
                  T_{\textit{Max Comm Old}}}
 \end{equation}
                = \frac{T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
                  T_{\textit{Max Comm Old}}}
 \end{equation}

-\begin{figure}
+\begin{figure*}

   \centering
   \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}
   \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
 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


@@ -398,13 +429,14 @@ objective of this paper and we choose Rauber's model as an example with two
 reasons that mentioned before.
 
 \section{Optimal Scaling Factor for Performance and Energy}
 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.
 
 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]
   \caption{EPSA}
   \label{EPSA}
   \begin{algorithmic}[1]


@@ -438,24 +470,29 @@ for each task from the first iteration only. When these times are measured, the
 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
 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
 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


@@ -470,6 +507,7 @@ have imbalanced workloads. Then EQ~(\ref{eq:fi}) works in adaptive way to change
 the frequency according to the nodes workloads.
 
 \section{Experimental Results}
 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
 
 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


@@ -484,16 +522,15 @@ detailed characteristics of our platform file are shown in the
 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.
 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
   \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
   \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}
     GHz& MHz&  & & &  &Duplex  \\\hline
   \end{tabular}
   \label{table:platform}


@@ -517,18 +554,18 @@ programs. In table~(\ref{table:factors results}), we record all optimal scaling
 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.
 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
   \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}
   \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
   \caption{Optimal Scaling Factors Results}
   % title of Table
   \centering


@@ -539,13 +576,13 @@ same time over all available scales.
     \hline
     Program & Optimal & Energy  & Performance&Energy-Perf.\\
     Name & Scaling Factor& Saving \%&Degradation \% &Distance  \\ \hline
     \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
     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
   \end{tabular}
   \label{table:factors results}
   % is used to refer this table in the text


@@ -560,6 +597,7 @@ cases. In EP there are no communications inside the iterations. This make our
 EPSA to selects smaller scaling factor values (inducing smaller energy savings).
 
 \section{Comparing Results}
 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
 
 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


@@ -571,48 +609,48 @@ scenario as $Rauber_{E-P}$. The comparison is made in tables~(\ref{table:compare
   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.
   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
   \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
     \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
     $Rauber_{E}$&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
 
     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
 
     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
 
     $Rauber_{E}$&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
 
     $Rauber_{E}$&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{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
   \caption{Comparing Results for The NAS Class B}
   % title of Table
   \centering


@@ -622,8 +660,8 @@ benchmarks programs for classes A,B and C.
     name &name&value& Saving \%&Degradation \% &Distance
     \\ \hline
     % \rowcolor[gray]{0.85}
     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
     $Rauber_{E}$&CG &2.15 &45.34&28.88&16.46\\ \hline
 
     EPSA&MG & 1.47 &34.98&18.35&16.63\\ \hline


@@ -631,30 +669,30 @@ benchmarks programs for classes A,B and C.
     $Rauber_{E}$&MG &2.14&43.56&37.07&6.49 \\ \hline
 
     EPSA&EP &1.08 &20.29&17.15&3.14 \\ \hline
     $Rauber_{E}$&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
 
     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
 
     $Rauber_{E}$&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
     $Rauber_{E-P}$&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{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
   \caption{Comparing Results for The NAS Class C}
   % title of Table
   \centering


@@ -666,35 +704,35 @@ benchmarks programs for classes A,B and C.
     % \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
     % \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
     $Rauber_{E}$&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{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
 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


@@ -716,26 +754,35 @@ concatenating with less performance degradation and this the objective of this
 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.
 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
   \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}
 
   \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}
 
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+%%%ispell-local-dictionary: "american"

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 %  LocalWords:  Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
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 %  LocalWords:  Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber