Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/mpi-energy

[mpi-energy.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 9310147fbab6b4cde5f7e6477433a9318bf806ef..e60d17b12394fd04f692ff516231af37f8680aa3 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -10,6 +10,9 @@
 \usepackage{colortbl}
 \usepackage{amsmath}
 
 \usepackage{colortbl}
 \usepackage{amsmath}
 

+\usepackage{url}
+\DeclareUrlCommand\email{\urlstyle{same}}
+

 \usepackage[autolanguage,np]{numprint}
 \renewcommand*\npunitcommand[1]{\text{#1}}
 
 \usepackage[autolanguage,np]{numprint}
 \renewcommand*\npunitcommand[1]{\text{#1}}
 


@@ -32,34 +35,23 @@
   \IEEEauthorblockA{%
     FEMTO-ST Institute\\
     University of Franche-Comté\\
   \IEEEauthorblockA{%
     FEMTO-ST Institute\\
     University of Franche-Comté\\

-<<<<<<< HEAD
-    IUT de Belfort-Montb\'{e}liard, Rue Engel Gros, BP 27, 90016 Belfort, France\\
-   Fax  : (+33)~3~84~58~77~32\\
-   Email: \{jean-claude.charr, raphael.couturier, ahmed.fanfakh, arnaud.giersch\}@univ-fcomte.fr
-=======

     IUT de Belfort-Montbéliard, 19 avenue du Maréchal Juin, BP 527, 90016 Belfort cedex, France\\
     IUT de Belfort-Montbéliard, 19 avenue du Maréchal Juin, BP 527, 90016 Belfort cedex, France\\

-    Fax  : +33~3~84~58~77~32\\
-    Email: \{jean-claude.charr,raphael.couturier,ahmed.fanfakh\_badri\_muslim,arnaud.giersch\}@univ-fcomte.fr
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
+   % Fax  : +33~3~84~58~77~32\\
+    Email: \email{{jean-claude.charr,raphael.couturier,ahmed.fanfakh_badri_muslim,arnaud.giersch}@univ-fcomte.fr}

    }
   }
 
 \maketitle
 
    }
   }
 
 \maketitle
 

-<<<<<<< HEAD
-=======
-\AG{Is the fax number correct? Shall we add a telephone number?}
-\JC{Use Capital letters for only the first letter in the title of a section, table, figure, ...} 
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 \begin{abstract}
   Dynamic Voltage Frequency Scaling (DVFS) can be applied to modern CPUs. 
 This technique is usually used to reduce the energy consumed by a CPU while
 computing . Indeed, power consumption by a processor at a given instant is
 exponentially related to its frequency. Thus, decreasing the frequency reduces
 the power consumed by the CPU. However, it can also significantly affect the
 \begin{abstract}
   Dynamic Voltage Frequency Scaling (DVFS) can be applied to modern CPUs. 
 This technique is usually used to reduce the energy consumed by a CPU while
 computing . Indeed, power consumption by a processor at a given instant is
 exponentially related to its frequency. Thus, decreasing the frequency reduces
 the power consumed by the CPU. However, it can also significantly affect the

-performance of the executed program if it is compute bound and a low CPU
+performance of the executed program if it is compute bound and if a low CPU

 frequency is selected. The performance degradation ratio can even be higher than
 frequency is selected. The performance degradation ratio can even be higher than

-the saved energy ratio. Therefore, the chosen scaling factor must give the best possible tradeoff
+the saved energy ratio. Therefore, the chosen scaling factor must give the best possible trade-off

 between energy reduction and performance. 
 
 In this paper we present an algorithm
 between energy reduction and performance. 
 
 In this paper we present an algorithm


@@ -113,16 +105,16 @@ 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 and Rünger methods~\cite{3}.
 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 and Rünger methods~\cite{3}.

-The comparison's results show that our algorithm gives better energy-time tradeoff.
-
-This paper is organized as follows: Section~\ref{sec.relwork} presents related works
-from other authors.  Section~\ref{sec.exe} shows the execution of parallel
-tasks and sources of idle times.  It resumes the energy
-model of homogeneous platform. Section~\ref{sec.mpip} evaluates the performance
-of MPI program.  Section~\ref{sec.compet} presents the energy-performance tradeoffs
-objective function. Section~\ref{sec.optim} demonstrates the proposed energy-performance algorithm. Section~\ref{sec.expe} verifies the performance prediction
-model and presents the results of the proposed algorithm.  Also, It shows the comparison results. Finally,
-we conclude in Section~\ref{sec.concl}.
+The comparison's results show that our algorithm gives better energy-time trade-off.
+
+This paper is organized as follows: Section~\ref{sec.relwork} presents some related works
+from other authors.  Section~\ref{sec.exe} explains the execution of parallel
+tasks and the sources of slack times.  It also presents an energy
+model for homogeneous platforms. Section~\ref{sec.mpip} describes how the performance
+of MPI programs can be predicted .  Section~\ref{sec.compet} presents the energy-performance 
+objective function that maximizes the reduction of energy consumption while minimizing the degradation of the program's performance. Section~\ref{sec.optim} details the proposed energy-performance algorithm. Section~\ref{sec.expe} verifies the accuracy of the performance prediction
+model and presents the results of the proposed algorithm.  It also shows the comparison results between our method and other existing methods. Finally,
+we conclude in Section~\ref{sec.concl} with a summary and some future works.

 \section{Related works}
 \label{sec.relwork}
 
 \section{Related works}
 \label{sec.relwork}
 


@@ -159,16 +151,16 @@ The main drawback for these methods is that they all require executing a part or
 The online scaling factor selection methods are executed during the runtime of the program. They are usually integrated into iterative programs where the same block of instructions is executed many times.  During the first few iterations, many informations are measured such as the execution time, the energy consumed using a multimeter, the slack times, ... Then a  method will exploit these measurements to compute the scaling factor values for each processor. This operation, measurements and computing new scaling factor, can be repeated as much as needed if the iterations are not regular. Kimura, Peraza, Yu-Liang et al.  ~\cite{11,2,31} used learning methods to select the appropriate scaling factor values  to eliminate the slack times during runtime. However, as seen in ~\cite{39,19}, machine learning methods can take a lot of time to converge when the number of available gears is big. To reduce the impact of slack times,  in~\cite{1}, Lim et al. developed an algorithm that detects the
 communication sections and changes the frequency during these sections
 only. This approach might change the frequency of each processor many times per iteration if an iteration
 The online scaling factor selection methods are executed during the runtime of the program. They are usually integrated into iterative programs where the same block of instructions is executed many times.  During the first few iterations, many informations are measured such as the execution time, the energy consumed using a multimeter, the slack times, ... Then a  method will exploit these measurements to compute the scaling factor values for each processor. This operation, measurements and computing new scaling factor, can be repeated as much as needed if the iterations are not regular. Kimura, Peraza, Yu-Liang et al.  ~\cite{11,2,31} used learning methods to select the appropriate scaling factor values  to eliminate the slack times during runtime. However, as seen in ~\cite{39,19}, machine learning methods can take a lot of time to converge when the number of available gears is big. To reduce the impact of slack times,  in~\cite{1}, Lim et al. developed an algorithm that detects the
 communication sections and changes the frequency during these sections
 only. This approach might change the frequency of each processor many times per iteration if an iteration

-contains more than one communication section. In ~\cite{3}, Rauber and Rünger used an analytical model that after measuring the energy consumed and the execution time with the highest frequency gear, it can predict the energy consumed and the execution time for every frequency gear .   These predictions may be used to choose the optimal gear for each processor executing the parallel program to reduce energy consumption. 
+contains more than one communication section. In ~\cite{3}, Rauber and Rünger used an analytical model that can predict the consumed energy  and the execution time for every frequency gear after measuring the consumed energy  and the execution time with the highest frequency gear.   These predictions may be used to choose the optimal gear for each processor executing the parallel program to reduce energy consumption. 

 To maintain the performance of the parallel program , they
 set the  processor with the biggest load to the highest gear and then compute the scaling  factor values for the rest of the processors. Although this model was built for parallel architectures, it can be adapted  to distributed architectures by taking into account the communications. 
 To maintain the performance of the parallel program , they
 set the  processor with the biggest load to the highest gear and then compute the scaling  factor values for the rest of the processors. Although this model was built for parallel architectures, it can be adapted  to distributed architectures by taking into account the communications. 

-The primary contribution of this paper is presenting a new online scaling factor selection method which has the following characteristics :
+The primary contribution of our paper is presenting a new online scaling factor selection method which has the following characteristics :

 \begin{enumerate}
 \begin{enumerate}

-\item Based on Rauber's analytical model to predict the energy consumption and the execution time of the application with different frequency gears. 
-\item Selects the frequency scaling factor for simultaneously optimizing energy reduction and maintaining performance.
-\item Well adapted to distributed architectures because it takes into account the communication time.
-\item Well adapted to distributed applications with imbalanced tasks.
-\item Has very small footprint when compared to other
+\item It is based on Rauber and Rünger analytical model to predict the energy consumption and the execution time of the application with different frequency gears. 
+\item It selects the frequency scaling factor for simultaneously optimizing energy reduction and maintaining performance.
+\item It is well adapted to distributed architectures because it takes into account the communication time.
+\item It is well adapted to distributed applications with imbalanced tasks.
+\item it has very small footprint when compared to other

   methods (e.g.,~\cite{19}) and does not require profiling or training as
   in~\cite{38,34}.
 \end{enumerate}
   methods (e.g.,~\cite{19}) and does not require profiling or training as
   in~\cite{38,34}.
 \end{enumerate}


@@ -176,13 +168,8 @@ The primary contribution of this paper is presenting a new online scaling factor
 
 \section{Execution and energy of parallel tasks on homogeneous platform} 
 \label{sec.exe}
 
 \section{Execution and energy of parallel tasks on homogeneous platform} 
 \label{sec.exe}

-<<<<<<< HEAD
-%\AG{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
+%\JC{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}

 \subsection{Parallel tasks execution on homogeneous platform}
 \subsection{Parallel tasks execution on homogeneous platform}

-=======
-\JC{The whole subsection ``Parallel Tasks Execution on Homogeneous Platform'', can be deleted if we need space, we can just say we are interested in this paper in homogeneous clusters}
-\subsection{Parallel Tasks Execution on Homogeneous Platform}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 A homogeneous cluster consists of identical nodes in terms of hardware and software. 
 Each node has its own memory and at least one processor which can
 be a multi-core. The nodes are connected via a high bandwidth network. Tasks
 A homogeneous cluster consists of identical nodes in terms of hardware and software. 
 Each node has its own memory and at least one processor which can
 be a multi-core. The nodes are connected via a high bandwidth network. Tasks


@@ -191,8 +178,8 @@ we consider execution of the synchronous tasks on distributed homogeneous
 platform. These tasks can exchange the data via synchronous message passing.
 \begin{figure*}[t]
   \centering
 platform. These tasks can exchange the data via synchronous message passing.
 \begin{figure*}[t]
   \centering

-  \subfloat[Sync. imbalanced communications]{\includegraphics[scale=0.67]{commtasks}\label{fig:h1}}
-  \subfloat[Sync. imbalanced computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
+  \subfloat[Sync. imbalanced communications]{\includegraphics[scale=0.67]{fig/commtasks}\label{fig:h1}}
+  \subfloat[Sync. imbalanced computations]{\includegraphics[scale=0.67]{fig/compt}\label{fig:h2}}

   \caption{Parallel tasks on homogeneous platform}
   \label{fig:homo}
 \end{figure*}
   \caption{Parallel tasks on homogeneous platform}
   \label{fig:homo}
 \end{figure*}


@@ -201,7 +188,7 @@ communication time. Moreover, the synchronous communications between tasks can
 lead to slack times while tasks wait at the synchronization barrier for other tasks to
 finish their tasks (see figure~(\ref{fig:h1})). The imbalanced communications 
 happen when nodes have to send/receive different amount of data or they communicate
 lead to slack times while tasks wait at the synchronization barrier for other tasks to
 finish their tasks (see figure~(\ref{fig:h1})). The imbalanced communications 
 happen when nodes have to send/receive different amount of data or they communicate

-with different number of nodes. Another source of idle times is the imbalanced computations.  
+with different number of nodes. Another source of slack times is the imbalanced computations.  

 This happens when processing different amounts of data on each processor  (see figure~(\ref{fig:h2})).  
 In this case the fastest tasks have to wait at the synchronization barrier for the 
 slowest ones to begin the next task. In both cases the overall execution time 
 This happens when processing different amounts of data on each processor  (see figure~(\ref{fig:h2})).  
 In this case the fastest tasks have to wait at the synchronization barrier for the 
 slowest ones to begin the next task. In both cases the overall execution time 


@@ -229,12 +216,13 @@ The static power $P_{static}$ captures the leakage power as follows:
 \end{equation}
 where V is the supply voltage, $N_{trans}$ is the number of transistors, $K_{design}$ is a
 design dependent parameter and $I_{leak}$ is a technology-dependent
 \end{equation}
 where V is the supply voltage, $N_{trans}$ is the number of transistors, $K_{design}$ is a
 design dependent parameter and $I_{leak}$ is a technology-dependent

-parameter. Energy consumed by an individual processor $E_{ind}$ is the summation
-of the dynamic and the static powers multiplied by the execution time~\cite{36,15}.
+parameter. The energy consumed by an individual processor to execute a given program can be computed as:

 \begin{equation}
   \label{eq:eind}
 \begin{equation}
   \label{eq:eind}

-   E_\textit{ind} = ( P_\textit{dyn} + P_\textit{static} ) \cdot T
+   E_\textit{ind} =  P_\textit{dyn} \cdot T_{Comp} + P_\textit{static} \cdot T

 \end{equation}
 \end{equation}

+where $T$ is the execution time of the program, $T_{Comp}$ is the computation time and $T_{Comp} \le T$. $T_{Comp}$ may be equal to $T$ if there is no communications, no slack times and no synchronizations. 
+

 DVFS is a process that is allowed in
 modern processors to reduce the dynamic power by scaling down the voltage and
 frequency. Its main objective is to reduce the overall energy
 DVFS is a process that is allowed in
 modern processors to reduce the dynamic power by scaling down the voltage and
 frequency. Its main objective is to reduce the overall energy


@@ -253,12 +241,8 @@ new frequency value~(\emph {P-state}) in the governor. The CPU governor is an
 interface driver supplied by the operating system's kernel to
 lower a core's frequency.  This factor reduces
 quadratically the dynamic power which may cause degradation in performance and thus, the increase of the static energy because the execution time is increased~\cite{36}. If the tasks are sorted according to their execution times before scaling in a descending order,   the total energy consumption model for a parallel
 interface driver supplied by the operating system's kernel to
 lower a core's frequency.  This factor reduces
 quadratically the dynamic power which may cause degradation in performance and thus, the increase of the static energy because the execution time is increased~\cite{36}. If the tasks are sorted according to their execution times before scaling in a descending order,   the total energy consumption model for a parallel

-homogeneous platform, as  presented by Rauber et al.~\cite{3}, can be written as a function of   the scaling factor \emph S,   as in EQ~(\ref{eq:energy}).
+homogeneous platform, as  presented by Rauber and Rünger~\cite{3}, can be written as a function of   the scaling factor \emph S,   as in EQ~(\ref{eq:energy}).

 
 

-<<<<<<< HEAD
-=======
-\JC{Are you sure of the following equation}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 \begin{equation}
   \label{eq:energy}
   E = P_\textit{dyn} \cdot S_1^{-2} \cdot
 \begin{equation}
   \label{eq:energy}
   E = P_\textit{dyn} \cdot S_1^{-2} \cdot


@@ -268,29 +252,16 @@ homogeneous platform, as  presented by Rauber et al.~\cite{3}, can be written as
 \end{equation}
 where \emph N is the number of parallel nodes,  $T_i  \  and  \  S_i \  for \  i=1,...,N$ are the execution times and scaling factors of the sorted tasks. Therefore,  $T1$ is the time of the slowest task,  and $S_1$ its scaling factor which should be the highest because they are proportional to
 the time values $T_i$.  The scaling factors are computed as in EQ~(\ref{eq:si}).
 \end{equation}
 where \emph N is the number of parallel nodes,  $T_i  \  and  \  S_i \  for \  i=1,...,N$ are the execution times and scaling factors of the sorted tasks. Therefore,  $T1$ is the time of the slowest task,  and $S_1$ its scaling factor which should be the highest because they are proportional to
 the time values $T_i$.  The scaling factors are computed as in EQ~(\ref{eq:si}).

-<<<<<<< HEAD
-=======
-\JC{This equation does not make sense either, what's S? there is no F}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 \begin{equation}
   \label{eq:si}
   S_i = S \cdot \frac{T_1}{T_i}
       = \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i}
 \end{equation}
 \begin{equation}
   \label{eq:si}
   S_i = S \cdot \frac{T_1}{T_i}
       = \frac{F_\textit{max}}{F_\textit{new}} \cdot \frac{T_1}{T_i}
 \end{equation}

-<<<<<<< HEAD

 In this paper we depend on
 In this paper we depend on

-=======
-\JC{The Rauber model was used for a parallel machine not a homogeneous platform}
-where $F$ is the number of available frequencies. In this paper we depend on
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 Rauber and Rünger energy model EQ~(\ref{eq:energy}) for two reasons: (1) this
 model is used for any number of concurrent tasks, and (2) we
 compare our algorithm with Rauber and Rünger scaling factor selection method which is based on
 EQ~(\ref{eq:energy}). The optimal scaling factor is computed by minimizing the derivation for this equation which produces EQ~(\ref{eq:sopt}).
 Rauber and Rünger energy model EQ~(\ref{eq:energy}) for two reasons: (1) this
 model is used for any number of concurrent tasks, and (2) we
 compare our algorithm with Rauber and Rünger scaling factor selection method which is based on
 EQ~(\ref{eq:energy}). The optimal scaling factor is computed by minimizing the derivation for this equation which produces EQ~(\ref{eq:sopt}).

-<<<<<<< HEAD
-=======
-\JC{what's the small n in the equation}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 
 \begin{equation}
   \label{eq:sopt}
 
 \begin{equation}
   \label{eq:sopt}


@@ -368,22 +339,23 @@ performance as follows:
 \begin{equation}
   \label{eq:pnorm_en}
   P^{-1}_\textit{Norm} = \frac{ T_\textit{Old}}{ T_\textit{New}}
 \begin{equation}
   \label{eq:pnorm_en}
   P^{-1}_\textit{Norm} = \frac{ T_\textit{Old}}{ T_\textit{New}}

-               = \frac{ T_\textit{Old}}{T_\textit{Max Comp Old} \cdot S +
+               = \frac{T_\textit{Max Comp Old} +
+                 T_\textit{Max Comm Old}}{T_\textit{Max Comp Old} \cdot S +

                  T_\textit{Max Comm Old}}
 \end{equation}
 \begin{figure*}
   \centering
   \subfloat[Converted relation.]{%
                  T_\textit{Max Comm Old}}
 \end{equation}
 \begin{figure*}
   \centering
   \subfloat[Converted relation.]{%

-    \includegraphics[width=.4\textwidth]{file.eps}\label{fig:r1}}%
+    \includegraphics[width=.4\textwidth]{fig/file}\label{fig:r1}}%

   \qquad%
   \subfloat[Real relation.]{%
   \qquad%
   \subfloat[Real relation.]{%

-    \includegraphics[width=.4\textwidth]{file3.eps}\label{fig:r2}}
+    \includegraphics[width=.4\textwidth]{fig/file3}\label{fig:r2}}

   \label{fig:rel}
   \caption{The energy and performance relation}
 \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
   \label{fig:rel}
   \caption{The energy and performance relation}
 \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
+curve EQ~(\ref{eq:pnorm_en}) over all available scaling factors. This represents

 the minimum energy consumption with minimum execution time (better performance)
 at the same time, see figure~(\ref{fig:r1}). Then our objective function has the
 following form:
 the minimum energy consumption with minimum execution time (better performance)
 at the same time, see figure~(\ref{fig:r1}). Then our objective function has the
 following form:


@@ -392,7 +364,7 @@ following form:
  Max Dist = \max_{j=1,2,\dots,F} (\overbrace{P^{-1}_\textit{Norm}(S_j)}^{\text{Maximize}} -
                         \overbrace{E_\textit{Norm}(S_j)}^{\text{Minimize}} )
 \end{equation}
  Max Dist = \max_{j=1,2,\dots,F} (\overbrace{P^{-1}_\textit{Norm}(S_j)}^{\text{Maximize}} -
                         \overbrace{E_\textit{Norm}(S_j)}^{\text{Minimize}} )
 \end{equation}

-where F is the number of available frequencies. Then we can select the optimal scaling factor that satisfy
+where F is the number of available frequencies. Then we can select the optimal scaling factor that satisfies

 EQ~(\ref{eq:max}).  Our objective function can work with any energy model or
 static power values stored in a data file. Moreover, this function works in
 optimal way when the energy curve has a convex form over the available frequency scaling
 EQ~(\ref{eq:max}).  Our objective function can work with any energy model or
 static power values stored in a data file. Moreover, this function works in
 optimal way when the energy curve has a convex form over the available frequency scaling


@@ -400,7 +372,7 @@ factors as shown in~\cite{15,3,19}.
 
 \section{Optimal scaling factor for performance and energy}
 \label{sec.optim}
 
 \section{Optimal scaling factor for performance and energy}
 \label{sec.optim}

- Algorithm~\ref{EPSA} compute the optimal scaling factor according to the objective function described above.
+ Algorithm~\ref{EPSA} computes the optimal scaling factor according to the objective function described above.

 \begin{algorithm}[tp]
   \caption{Scaling factor selection algorithm}
   \label{EPSA}
 \begin{algorithm}[tp]
   \caption{Scaling factor selection algorithm}
   \label{EPSA}


@@ -432,11 +404,24 @@ factors as shown in~\cite{15,3,19}.
 
 The proposed algorithm works online during the execution time of the MPI
 program. It selects the optimal scaling factor after gathering the computation and communication times 
 
 The proposed algorithm works online during the execution time of the MPI
 program. It selects the optimal scaling factor after gathering the computation and communication times 

-from the program after one iteration. Then the program changes the new frequencies of the CPUs according to the computed scaling factors. This algorithm has small execution time
-(between 0.00152 $ms$ for 4 nodes to 0.00665 $ms$ for 32 nodes). The algorithm complexity is O(F$\cdot$N), 
+from the program after one iteration. Then the program changes the new frequencies of the CPUs according to the computed scaling factors. This algorithm has a small execution time: for a homogeneous cluster composed of nodes having the characteristics presented in table~\ref{table:platform}, it takes  0.00152 $ms$ on average for 4 nodes and 0.00665 $ms$ on average for 32 nodes. The algorithm complexity is O(F$\cdot$N), 

 where F is the number of available frequencies and N is the number of computing nodes.  The algorithm is called just 
 once during the execution of the program. The DVFS algorithm~(\ref{dvfs}) shows where and when the algorithm is called
 in the MPI program.
 where F is the number of available frequencies and N is the number of computing nodes.  The algorithm is called just 
 once during the execution of the program. The DVFS algorithm~(\ref{dvfs}) shows where and when the algorithm is called
 in the MPI program.

+\begin{table}[htb]
+  \caption{Platform file parameters}
+  % title of Table
+  \centering
+  \begin{tabular}{|*{7}{l|}}
+    \hline
+    Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
+    Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy  \\ \hline
+    \np{2.5} & \np{800} & \np[GBps]{2.25} &\np[$\mu$s]{0.5}& \np[GBps]{1} & \np[$\mu$s]{50} &Full  \\
+    GHz& MHz&  & & &  &Duplex  \\\hline
+  \end{tabular}
+  \label{table:platform}
+\end{table}
+

 %\begin{minipage}{\textwidth}
 
 \begin{algorithm}[tp]
 %\begin{minipage}{\textwidth}
 
 \begin{algorithm}[tp]


@@ -444,8 +429,8 @@ in the MPI program.
   \label{dvfs}
   \begin{algorithmic}[1]
  \For {$k:=1$ to $Some-Iterations \; $}
   \label{dvfs}
   \begin{algorithmic}[1]
  \For {$k:=1$ to $Some-Iterations \; $}

-  \State -Computations Section.
-   \State -Communications Section.
+  \State -Computations section.
+   \State -Communications section.

    \If {$(k=1)$} 
      \State -Gather all times of computation and\par\hspace{13 pt} communication from each node.
      \State -Call algorithm~\ref{EPSA} with these times.
    \If {$(k=1)$} 
      \State -Gather all times of computation and\par\hspace{13 pt} communication from each node.
      \State -Call algorithm~\ref{EPSA} with these times.


@@ -478,19 +463,7 @@ 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. The simulated network link is 1 GB Ethernet (TCP/IP). 
 The backbone of the cluster simulates a high performance switch.
 from 2.5 GHz to 800 MHz with 100 MHz difference between each two successive
 frequencies. The simulated network link is 1 GB Ethernet (TCP/IP). 
 The backbone of the cluster simulates a high performance switch.

-\begin{table}[htb]
-  \caption{Platform file parameters}
-  % title of Table
-  \centering
-  \begin{tabular}{|*{7}{l|}}
-    \hline
-    Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
-    Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy  \\ \hline
-    \np{2.5} & \np{800} & \np[GBps]{2.25} &\np[$\mu$s]{0.5}& \np[GBps]{1} & \np[$\mu$s]{50} &Full  \\
-    GHz& MHz&  & & &  &Duplex  \\\hline
-  \end{tabular}
-  \label{table:platform}
-\end{table}
+

 \subsection{Performance prediction verification}
 
 In this section we evaluate the precision of our performance prediction method based on EQ~(\ref{eq:tnew}) by applying it the NAS benchmarks. The NAS programs are executed with the class B option for comparing the
 \subsection{Performance prediction verification}
 
 In this section we evaluate the precision of our performance prediction method based on EQ~(\ref{eq:tnew}) by applying it the NAS benchmarks. The NAS programs are executed with the class B option for comparing the


@@ -500,26 +473,19 @@ time values. These scaling factors are computed by dividing the maximum
 frequency by the new one see EQ~(\ref{eq:s}). 
 \begin{figure*}[t]
   \centering
 frequency by the new one see EQ~(\ref{eq:s}). 
 \begin{figure*}[t]
   \centering

-  \includegraphics[width=.328\textwidth]{cg_per.eps}\hfill%
-  \includegraphics[width=.328\textwidth]{mg_pre.eps}\hfill%
- % \includegraphics[width=.4\textwidth]{bt_pre.eps}\qquad%
-  \includegraphics[width=.328\textwidth]{lu_pre.eps}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/cg_per}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/mg_pre}\hfill%
+ % \includegraphics[width=.4\textwidth]{fig/bt_pre}\qquad%
+  \includegraphics[width=.328\textwidth]{fig/lu_pre}\hfill%

   \caption{Comparing predicted to real execution time}
   \label{fig:pred}
 \end{figure*}
 %see Figure~\ref{fig:pred}
 In our cluster there are 18 available frequency states for each processor. 
   \caption{Comparing predicted to real execution time}
   \label{fig:pred}
 \end{figure*}
 %see Figure~\ref{fig:pred}
 In our cluster there are 18 available frequency states for each processor. 

-This lead to 18 run states for each program. We use seven MPI programs of the
+This leads to 18 run states for each program. We use seven MPI programs of the

  NAS parallel benchmarks: CG, MG, EP, FT, BT, LU
  NAS parallel benchmarks: CG, MG, EP, FT, BT, LU

-<<<<<<< HEAD

 and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The maximum normalized error between the predicted execution time and the real time (SimGrid time) for all programs is between 0.0073 to 0.031. The  better case is for CG and the worse case is for LU. 
 \subsection{The experimental results for the scaling algorithm }
 and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The maximum normalized error between the predicted execution time and the real time (SimGrid time) for all programs is between 0.0073 to 0.031. The  better case is for CG and the worse case is for LU. 
 \subsection{The experimental results for the scaling algorithm }

-=======
-and SP. Figure~(\ref{fig:pred}) presents plots of the real execution times and the simulated ones. The average normalized errors between the predicted execution time and
-the real time (SimGrid time) for all programs is between 0.0032 to 0.0133. 
-\JC{why compute the average error not the max}
-\subsection{The  experimental results}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 The proposed algorithm was applied to seven MPI programs of the NAS
 benchmarks (EP, CG, MG, FT, BT, LU and SP) which were run with three classes (A, B and
 C). For each instance the benchmarks were executed on a number of processors
 The proposed algorithm was applied to seven MPI programs of the NAS
 benchmarks (EP, CG, MG, FT, BT, LU and SP) which were run with three classes (A, B and
 C). For each instance the benchmarks were executed on a number of processors


@@ -530,7 +496,7 @@ respectively.
 Depending on EQ~(\ref{eq:energy}), we measure the energy consumption for all
 the NAS MPI programs while assuming the power dynamic with the highest frequency is equal to \np[W]{20} and
 the power static is equal to \np[W]{4} for all experiments. These power values were also
 Depending on EQ~(\ref{eq:energy}), we measure the energy consumption for all
 the NAS MPI programs while assuming the power dynamic with the highest frequency is equal to \np[W]{20} and
 the power static is equal to \np[W]{4} for all experiments. These power values were also

-used by Rauber and Rünger in~\cite{3}.   The results showed that the algorithm selected
+used by Rauber and Rünger in~\cite{3}.  The results showed that the algorithm selected

 different scaling factors for each program depending on the communication
 features of the program as in the plots~(\ref{fig:nas}). These plots illustrate that
 there are different distances between the normalized energy and the normalized
 different scaling factors for each program depending on the communication
 features of the program as in the plots~(\ref{fig:nas}). These plots illustrate that
 there are different distances between the normalized energy and the normalized


@@ -548,12 +514,12 @@ energy saving percent and the minimum performance degradation percent at the
 same time from all available scaling factors.
 \begin{figure*}[t]
   \centering
 same time from all available scaling factors.
 \begin{figure*}[t]
   \centering

-  \includegraphics[width=.328\textwidth]{ep.eps}\hfill%
-  \includegraphics[width=.328\textwidth]{cg.eps}\hfill%
-  \includegraphics[width=.328\textwidth]{sp.eps}
-  \includegraphics[width=.328\textwidth]{lu.eps}\hfill%
-  \includegraphics[width=.328\textwidth]{bt.eps}\hfill%
-  \includegraphics[width=.328\textwidth]{ft.eps}
+  \includegraphics[width=.328\textwidth]{fig/ep}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/cg}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/sp}
+  \includegraphics[width=.328\textwidth]{fig/lu}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/bt}\hfill%
+  \includegraphics[width=.328\textwidth]{fig/ft}

   \caption{Optimal scaling factors for the predicted energy and performance of NAS benchmarks}
   \label{fig:nas}
 \end{figure*}
   \caption{Optimal scaling factors for the predicted energy and performance of NAS benchmarks}
   \label{fig:nas}
 \end{figure*}


@@ -592,14 +558,11 @@ optimal level without considering the performance as in EQ~(\ref{eq:sopt}). We
 refer to this scenario as $R_{E}$. The second scenario is similar to the first
 except setting the slower task to the maximum frequency (when the scale $S=1$)
 to keep the performance from degradation as mush as possible. We refer to this
 refer to this scenario as $R_{E}$. The second scenario is similar to the first
 except setting the slower task to the maximum frequency (when the scale $S=1$)
 to keep the performance from degradation as mush as possible. We refer to this

-<<<<<<< HEAD
-scenario as $R_{E-P}$. While we refer to our algorithm as EPSA. The comparison is made in tables~(\ref{table:compareA},\ref{table:compareB},\ref{table:compareC}). These
-=======
-scenario as $R_{E-P}$. The comparison is made in tables~(\ref{table:compareA},
-\ref{table:compareB}, and \ref{table:compareC}). These
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b
+scenario as $R_{E-P}$. While we refer to our algorithm as EPSA (Energy to Performance Scaling Algorithm). The comparison
+is made in tables \ref{table:compareA}, \ref{table:compareB},
+and~\ref{table:compareC}. These

 tables show the results of our method and Rauber and Rünger scenarios for all the
 tables show the results of our method and Rauber and Rünger scenarios for all the

-NAS benchmarks programs for classes A,B and C.
+NAS benchmarks programs for classes A, B and C.

 \begin{table}[p]
   \caption{Comparing results for  the NAS class A}
   % title of Table
 \begin{table}[p]
   \caption{Comparing results for  the NAS class A}
   % title of Table


@@ -724,38 +687,31 @@ NAS benchmarks programs for classes A,B and C.
 \label{table:compareC}
 % is used to refer this table in the text
 \end{table}
 \label{table:compareC}
 % is used to refer this table in the text
 \end{table}

-As shown in tables~\ref{table:compareA},~\ref{table:compareB} and~\ref{table:compareC}, the ($R_{E-P}$) method outperforms the ($R_{E}$) method in terms of performance and energy reduction. The ($R_{E-P}$) method also gives better energy savings than our method. However, although our scaling factor is not optimal for energy reduction, the results in these tables prove that our algorithm returns the best scaling factor that satisfy our objective method : the largest distance between energy reduction and performance degradation. 
-
-Figure~(\ref{fig:compare}) shows the maximum distance between the energy saving
-percent and the performance degradation percent.  
-Negative values mean that one of the two objectives (energy or performance) have been degraded more than the other. The positive tradeoffs with the highest values lead to maximum energy savings
+As shown in tables~\ref{table:compareA},~\ref{table:compareB} and~\ref{table:compareC}, the ($R_{E-P}$) method outperforms the ($R_{E}$) method in terms of performance and energy reduction. The ($R_{E-P}$) method also gives better energy savings than our method. However, although our scaling factor is not optimal for energy reduction, the results in these tables prove that our algorithm returns the best scaling factor that satisfy our objective method : the largest distance between energy reduction and performance degradation. Negative values in the energy-performance column mean that one of the two objectives (energy or performance) have been degraded more than the other. The positive trade-offs with the highest values lead to maximum energy savings

 while keeping the performance degradation as low as possible. Our algorithm always
 while keeping the performance degradation as low as possible. Our algorithm always

-gives the highest positive energy to performance tradeoffs while Rauber and Rünger method
-($R_{E-P}$) gives in some time negative tradeoffs such as in BT and
+gives the highest positive energy to performance trade-offs while Rauber and Rünger method
+($R_{E-P}$) gives in some time negative trade-offs such as in BT and

 EP.
 EP.

-\begin{figure*}[t]
-  \centering
-  \includegraphics[width=.328\textwidth]{compare_class_A.pdf}
-  \includegraphics[width=.328\textwidth]{compare_class_B.pdf}
-  \includegraphics[width=.328\textwidth]{compare_class_c.pdf}
-  \caption{Comparing our method to Rauber and Rünger methods}
-  \label{fig:compare}
-\end{figure*}
+%\begin{figure*}[t]
+%  \centering
+%  \includegraphics[width=.328\textwidth]{fig/compare_class_A}
+%  \includegraphics[width=.328\textwidth]{fig/compare_class_B}
+%  \includegraphics[width=.328\textwidth]{fig/compare_class_C}
+%  \caption{Comparing our method to Rauber and Rünger methods}
+%  \label{fig:compare}
+%\end{figure*}

 \section{Conclusion}
 \label{sec.concl}
 \section{Conclusion}
 \label{sec.concl}

-In this paper, we have presented a new online scaling factor selection method that optimizes simultaneously the energy and performance of a distributed application running on an homogeneous cluster. It uses the computation and communication times measured at the first iteration to predict energy consumption and the performance of the parallel application at every available frequency. Then, it selects the scaling factor that gives the best tradeoff between energy reduction and performance which is the maximum distance between the energy and the inverted performance curves. To evaluate this method, we have applied it to the NAS benchmarks and it was compared to Rauber and Rünger methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber and Rünger methods in terms of energy-performance ratio. 
+In this paper, we have presented a new online scaling factor selection method that optimizes simultaneously the energy and performance of a distributed application running on an homogeneous cluster. It uses the computation and communication times measured at the first iteration to predict energy consumption and the performance of the parallel application at every available frequency. Then, it selects the scaling factor that gives the best trade-off between energy reduction and performance which is the maximum distance between the energy and the inverted performance curves. To evaluate this method, we have applied it to the NAS benchmarks and it was compared to Rauber and Rünger methods while being executed on the simulator SimGrid. The results showed that our method, outperforms Rauber and Rünger methods in terms of energy-performance ratio. 

 
 In the near future, we would like to adapt this scaling factor selection method to heterogeneous platforms where each node has different characteristics. In particular, each CPU has different available frequencies, energy consumption and performance. It would be also interesting to develop a new energy model for asynchronous parallel iterative methods where the number of iterations is not known in advance and depends on the global convergence of the iterative system.
 
 
 \section*{Acknowledgment}
 
 In the near future, we would like to adapt this scaling factor selection method to heterogeneous platforms where each node has different characteristics. In particular, each CPU has different available frequencies, energy consumption and performance. It would be also interesting to develop a new energy model for asynchronous parallel iterative methods where the number of iterations is not known in advance and depends on the global convergence of the iterative system.
 
 
 \section*{Acknowledgment}

-As a PhD student, M. Ahmed Fanfakh, would like to thank the University of
+Computations have been performed on the supercomputer facilities of the
+Mésocentre de calcul de Franche-Comté. As a PhD student, M. Ahmed Fanfakh, would like to thank the University of

 Babylon (Iraq) for supporting his work.
 
 Babylon (Iraq) for supporting his work.
 

-<<<<<<< HEAD
-=======
-\JC{delete the online paths for each reference\AG{except for TOP500 and the NPB}}
->>>>>>> a61f50d29efe27025514a6a5e34444845de7fe9b

 % trigger a \newpage just before the given reference
 % number - used to balance the columns on the last page
 % adjust value as needed - may need to be readjusted if
 % trigger a \newpage just before the given reference
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@@ -774,4 +730,4 @@ Babylon (Iraq) for supporting his work.
 %%% End:
 
 %  LocalWords:  Fanfakh Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
 %%% End:
 
 %  LocalWords:  Fanfakh Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber

-%  LocalWords:  CMOS EQ EPSA Franche Comté Tflop Rünger
+%  LocalWords:  CMOS EQ EPSA Franche Comté Tflop Rünger IUT Maréchal Juin cedex