\section*{Journal Articles}
\begin{enumerate}[$\lbrack$1$\rbrack$]
-\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier, Arnaud Giersch. Optimizing Energy Consumption with
- DVFS for Message Passing Iterative Applications on Grid Architectures. \textit{Journal of Computational
- Science, 2016, ($1^{st}$ Revision Submitted)}
+\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier, Arnaud Giersch.Optimizing the energy consumption of message passing applications with iterations executed over grids. \textit{Journal of Computational
+ Science}, 2016.
\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier, Arnaud Giersch. Energy Consumption Reduction for
- Asynchronous Message Passing Applications. \textit{Journal of Supercomputing, 2016, (Submitted)}
+ Asynchronous Message Passing Applications. \textit{Journal of Supercomputing}, 2016, (Submitted)
\end{enumerate}
\end{enumerate}
-\cleardoublepage
\ No newline at end of file
+\cleardoublepage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\emph{ \begin{center} \Large Title \end{center}}
+\emph{ \begin{center} \Large Optimisation de la consommation énergétique des applications parallèles avec des itérations en réduisant la fréquence des processeurs \end{center}}
%\emph{ \begin{center} \large By \end{center}}
\emph{ \begin{center} \large Ahmed Badri Muslim Fanfakh \\ Université de Franche-Comt\'e, 2016 \end{center}}
%\emph{ \begin{center} \large The University of Franche-Comt\'e, 2015 \end{center}}
-\emph{ \begin{center} \large Encadrants: Raphaël Couturier, Jean-Claude Charr and Arnaud Giersch \end{center}}
+\emph{ \begin{center} \large Encadrants: Raphaël Couturier and Jean-Claude Charr \end{center}}
+Au cours des dernières années, l'informatique “green” est devenue un sujet important dans le calcul intensif. Cependant, les plates-formes informatiques continuent de consommer de plus en plus d'énergie en raison de l'augmentation du nombre de noeuds qui les composent. Afin de minimiser les coûts d'exploitation de ces plates-formes de nombreuses techniques ont été étudiées, parmi celles-ci, il y a le changement de la fréquence dynamique des processeurs (DVFS en anglais). Il permet de réduire la consommation d'énergie d'un CPU, en abaissant sa fréquence. Cependant, cela augmente le temps d'exécution de l'application. Par conséquent, il faut trouver un seuil qui donne le meilleur compromis entre la consommation d'énergie et la performance d'une application. Cette thèse présente des algorithmes développés pour optimiser la consommation d'énergie et les performances des applications parallèles avec des itérations synchrones et asynchrones sur des clusters ou des grilles. Les modèles de consommation d'énergie et de performance proposés pour chaque type d'application parallèle permettent de prédire le temps d'exécution et la consommation d'énergie d'une application pour toutes les fréquences disponibles.
+La contribution de cette thèse peut être divisé en trois parties. Tout d'abord, il s'agit d'optimiser le compromis entre la consommation d'énergie et les performances des applications parallèles avec des itérations synchrones sur des clusters homogènes. Deuxièmement, nous avons adapté les modèles de performance énergétique aux plates-formes hétérogènes dans lesquelles chaque noeud peut avoir des spécifications différentes telles que la puissance de calcul, la consommation d'énergie, différentes fréquences de fonctionnement ou encore des latences et des bandes passantes réseaux différentes. L'algorithme d'optimisation de la fréquence CPU a également été modifié en fonction de l'hétérogénéité de la plate-forme. Troisièmement, les modèles et l'algorithme d'optimisation de la fréquence CPU ont été complètement repensés pour prendre en considération les spécificités des algorithmes itératifs asynchrones.
+Tous ces modèles et algorithmes ont été appliqués sur des applications parallèles utilisant la bibliothèque MPI et ont été exécutés avec le simulateur Simgrid ou sur la plate-forme Grid'5000. Les expériences ont montré que les algorithmes proposés sont plus efficaces que les méthodes existantes. Ils n’introduisent qu’un faible surcoût et ne nécessitent pas de profilage au préalable car ils sont exécutés au cours du déroulement de l’application.
-\textbf{MOTS-CLÉS:} cl1, cl2, ...
-%Algorithmes distribués, Algorithmes centralisés, Robustesse, Connectivité, Efficacité énergétique, \'Energie des réseaux hétérogènes, Réseaux homogènes, Simulation des Réseaux, Evaluation de Performance, Les Communications sans Fil Ecologiques et le Réseautage
\ No newline at end of file
+\textbf{MOTS-CLÉS:} l'ajustement dynamique de la tension et de la fréquence d'un processeur, Grille de calcul, l'optimisation de l'énergie des applications parallèles avec des itérations.
+
+%Algorithmes distribués, Algorithmes centralisés, Robustesse, Connectivité, Efficacité énergétique, \'Energie des réseaux hétérogènes, Réseaux homogènes, Simulation des Réseaux, Evaluation de Performance, Les Communications sans Fil Ecologiques et le Réseautage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\include{Abstruct}
-%\include{Resume}
+\include{Resume}
%% Sommaire
\tableofcontents
%Committee:\\
%%--------------------
%% Set the English abstract
-\thesisabstract[english]{ English abstract
+\thesisabstract[english]{ This thesis, presents the algorithms developed to optimize the energy consumption
+and the performance of synchronous and asynchronous message passing applications with iterations running over clusters or grids. The energy consumption and performance models for each type of parallel application predicts its execution time and energy consumption for any selected frequency
+according to the characteristics of both the application and the architecture executing this application.
+
+
+The contribution of this thesis can be divided into three parts: Firstly, optimizing the trade-off between
+the energy consumption and the performance of the message passing applications with synchronous iterations
+running over homogeneous clusters. Secondly, adapting the energy and performance models to heterogeneous platforms where each node can have different specifications such as computing power, energy consumption, available frequency gears or network's latency and bandwidth. The frequency scaling algorithm was also modified to suit the heterogeneity of the platform. Thirdly, the models and the frequency scaling algorithm were completely rethought to take into considerations the asynchronism in the communication and computation.
+All these models and algorithms were applied to message passing applications with iterations and evaluated
+over either SimGrid simulator or Grid'5000 platform. The experiments showed that the proposed algorithms are
+efficient and outperform existing methods such as the energy and delay product. They also introduce a small
+runtime overhead and work online without any training or profiling.
+
}
-\thesiskeywords[english]{ kw1, kw2, ...}
+\thesiskeywords[english]{Dynamic voltage and frequency scaling, Grid computing, Energy optimization, parallel applications with iterations and online frequency scaling algorithm. }
-
+ \vspace{-5cm}
%%--------------------
%% Set the French abstract
-\thesisabstract[french]{ French abstract
+\thesisabstract[french]{Cette thèse présente des algorithmes développés pour optimiser la consommation d'énergie et les performances des applications parallèles avec des itérations synchrones et asynchrones sur des clusters ou des grilles. Les modèles de consommation d'énergie et de performance proposés pour chaque type d'application parallèle permettent de prédire le temps d'exécution et la consommation d'énergie d'une application pour toutes les fréquences disponibles. La contribution de cette thèse peut être divisé en trois parties. Tout d'abord, il s'agit d'optimiser le compromis entre la consommation d'énergie et les performances des applications parallèles avec des itérations synchrones sur des clusters homogènes. Deuxièmement, nous avons adapté les modèles de performance énergétique aux plates-formes hétérogènes dans lesquelles chaque noeud peut avoir des spécifications différentes telles que la puissance de calcul, la consommation d'énergie, différentes fréquences de fonctionnement ou encore des latences et des bandes passantes réseaux différentes. L'algorithme d'optimisation de la fréquence CPU a également été modifié en fonction de l'hétérogénéité de la plate-forme. Troisièmement, les modèles et l'algorithme d'optimisation de la fréquence CPU ont été complètement repensés pour prendre en considération les spécificités des algorithmes itératifs asynchrones.
+Tous ces modèles et algorithmes ont été appliqués sur des applications parallèles utilisant la bibliothèque MPI et ont été exécutés avec le simulateur Simgrid ou sur la plate-forme Grid'5000. Les expériences ont montré que les algorithmes proposés sont plus efficaces que les méthodes existantes. Ils n’introduisent qu’un faible surcoût et ne nécessitent pas de profilage au préalable car ils sont exécutés au cours du déroulement de l’application.
}
-\thesiskeywords[french]{cl1, cl2, ... }
+\thesiskeywords[french]{l'ajustement dynamique de la tension et de la fréquence d'un processeur, Grille de calcul, Optimisation de l'énergie, applications parallèles avec des itérations et
+en ligne algorithme fréquence ajustement.
+}
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--- /dev/null
+\BOOKMARK [2][]{Outline0.1}{Introduction and Problem definition}{}% 1
+\BOOKMARK [2][]{Outline0.2}{Using the energy reduction method}{}% 2
+\BOOKMARK [2][]{Outline0.3}{Contributions}{}% 3
+\BOOKMARK [3][]{Outline0.3.1.8}{3.1 Energy optimization of homogeneous platform}{Outline0.3}% 4
+\BOOKMARK [3][]{Outline0.3.2.22}{3.2 Energy optimization of heterogeneous platform}{Outline0.3}% 5
+\BOOKMARK [3][]{Outline0.3.3.40}{3.3 Energy optimization of asynchronous applications}{Outline0.3}% 6
+\BOOKMARK [2][]{Outline0.4}{Conclusions}{}% 7
+\BOOKMARK [2][]{Outline0.5}{Perspectives}{}% 8
--- /dev/null
+\beamer@slide {fig:h1}{10}
+\beamer@slide {fig:h2}{10}
+\beamer@slide {fig:homo}{10}
+\beamer@slide {eq:pd}{11}
+\beamer@slide {eq:ps}{11}
+\beamer@slide {fig:r2}{14}
+\beamer@slide {fig:r1}{14}
+\beamer@slide {fig:rel}{14}
+\beamer@slide {fig:heter}{24}
+\beamer@slide {eq:perf}{24}
+\beamer@slide {eq:max}{27}
+\beamer@slide {eq:perf}{36}
+\beamer@slide {eq:energy}{36}
+\beamer@slide {eq:max}{36}
+\beamer@slide {eq:asyn_time}{44}
+\beamer@slide {eq:asyn_perf}{44}
+\beamer@slide {eq:asyn_energy1}{45}
--- /dev/null
+ \documentclass{beamer}
+\usepackage{beamerthemefemto}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\DeclareGraphicsExtensions{.jpg, .png , .pdf, .bmp, .pdftex}
+\usepackage{algorithm,algorithmicx,algpseudocode}
+\usepackage{graphicx,graphics}
+\usepackage{subfig}
+\usepackage{listings}
+\usepackage{colortbl}
+\usepackage{amsmath}
+\usepackage{xspace}
+ \usepackage{movie15}
+ \usepackage{animate}
+\usepackage{xmpmulti}
+ \newcommand{\AG}[2][inline]{%
+ \todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}
+\newcommand{\JC}[2][inline]{%
+ \todo[color=red!10,#1]{\sffamily\textbf{JC:} #2}\xspace}
+\definecolor{myblue}{RGB}{0,29,119}
+\newcommand{\Xsub}[2]{{\ensuremath{#1_\mathit{#2}}}}
+
+%% used to put some subscripts lower, and make them more legible
+\newcommand{\fxheight}[1]{\ifx#1\relax\relax\else\rule{0pt}{1.52ex}#1\fi}
+
+\newcommand{\CL}{\Xsub{C}{L}}
+\newcommand{\Dist}{\mathit{Dist}}
+\newcommand{\EdNew}{\Xsub{E}{dNew}}
+\newcommand{\Eind}{\Xsub{E}{ind}}
+\newcommand{\Enorm}{\Xsub{E}{Norm}}
+\newcommand{\Eoriginal}{\Xsub{E}{Original}}
+\newcommand{\Ereduced}{\Xsub{E}{Reduced}}
+\newcommand{\Es}{\Xsub{E}{S}}
+\newcommand{\Fdiff}[1][]{\Xsub{F}{diff}_{\!#1}}
+\newcommand{\Fmax}[1][]{\Xsub{F}{max}_{\fxheight{#1}}}
+\newcommand{\Fnew}{\Xsub{F}{new}}
+\newcommand{\Vnew}{\Xsub{V}{new}}
+\newcommand{\Vmax}{\Xsub{V}{max}}
+\newcommand{\Ileak}{\Xsub{I}{leak}}
+\newcommand{\Kdesign}{\Xsub{K}{design}}
+\newcommand{\MaxDist}{\mathit{Max}\Dist}
+\newcommand{\MinTcm}{\mathit{Min}\Tcm}
+\newcommand{\Ntrans}{\Xsub{N}{trans}}
+\newcommand{\Pd}[1][]{\Xsub{P}{d}_{\fxheight{#1}}}
+\newcommand{\PdNew}{\Xsub{P}{dNew}}
+
+\newcommand{\PdOld}{\Xsub{P}{dOld}}
+\newcommand{\Pnorm}{\Xsub{P}{Norm}}
+\newcommand{\Tnorm}{\Xsub{T}{Norm}}
+\newcommand{\Ps}[1][]{\Xsub{P}{s}_{\fxheight{#1}}}
+\newcommand{\Scp}[1][]{\Xsub{S}{cp}_{#1}}
+\newcommand{\Sopt}[1][]{\Xsub{S}{opt}_{#1}}
+\newcommand{\Tcm}[1][]{\Xsub{T}{cm}_{\fxheight{#1}}}
+\newcommand{\Tcp}[1][]{\Xsub{T}{cp}_{#1}}
+\newcommand{\TcpOld}[1][]{\Xsub{T}{cpOld}_{#1}}
+\newcommand{\Tnew}{\Xsub{T}{New}}
+\newcommand{\Told}{\Xsub{T}{Old}}
+\newcommand{\Ltcm}[1][]{\Xsub{L}{tcm}_{\fxheight{#1}}}
+\newcommand{\Etcm}[1][]{\Xsub{E}{tcm}_{\fxheight{#1}}}
+\newcommand{\Niter}[1][]{\Xsub{N}{iter}_{\fxheight{#1}}}
+\newcommand{\Pmax}[1][]{\Xsub{P}{max}_{\fxheight{#1}}}
+\newcommand{\Pidle}[1][]{\Xsub{P}{idle}_{\fxheight{#1}}}
+ \usepackage{pifont}
+\usepackage{xcolor}
+\definecolor{myblue}{RGB}{0,29,119}
+\usepackage[textsize=footnotesize]{todonotes}
+\newcommand{\bsquare}{\item[\color{myblue}\ding{110}]}
+\newcommand{\barrow}{\item[\color{myblue}\ding{228}]}
+\newcommand{\bwarrow}{\item[\color{myblue}\ding{227}]}
+\DeclareGraphicsExtensions{.jpg, .png , .pdf, .bmp, .pdftex}
+
+
+
+%\title{Energy Consumption Optimization of Parallel Applications with
+%Iterations using CPU Frequency Scaling}
+\vspace{2cm}
+
+\title{ \textbf{Energy Consumption Optimization of Parallel Applications with Iterations using CPU Frequency Scaling} \\ \vspace{0.2cm} \hspace{1.8cm}\textbf{\textcolor{cyan}{\small PhD Dissertation Defense}}}\vspace{-1cm}
+\author{ \textbf{Ahmed Badri Muslim Fanfakh} \\ \vspace{0.5cm}\small Under Supervision: \textcolor{cyan}{\small Raphaël COUTURIER and Jean-Claude CHARR} \\\vspace{0.1cm} \textcolor{blue}{ University of Franche-Comté - FEMTO-ST - DISC Dept. - AND Team} \\ ~~~~~~~~~~~~~~~~~~~~~ \textbf{\textcolor{blue}{ 17 October 2016 }}}
+
+\date{}
+\vspace{-3cm}
+% ____ _____ ____ _ _ _____
+% | _ \| ____| __ )| | | |_ _|
+% | | | | _| | _ \| | | | | |
+% | |_| | |___| |_) | |_| | | |
+% |____/|_____|____/ \___/ |_|
+%
+\begin{document}
+\setbeamertemplate{background}{\titrefemto}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 01 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[plain]
+\vspace{1cm}
+\centering
+ \titlepage
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 02 %%
+%%%%%%%%%%%%%%%%%%%%
+\setbeamertemplate{background}{\pagefemto}
+\begin{frame}{Outline}
+
+\setbeamertemplate{section in toc}[sections numbered]
+\tableofcontents
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 03 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Introduction and problem definition}
+ \section{\small {Introduction and Problem definition}}
+ \bf \textcolor{blue}{Approaches to increase the computing power:}
+ \begin{minipage}{0.5\textwidth}
+ \textcolor{blue}{1)} \small \bf \textcolor{black}{Increasing the frequency of processor}
+ \end{minipage}%
+ \begin{minipage}{0.6\textwidth}
+
+\begin{figure}[h!]
+
+ \includegraphics[width=0.7\textwidth]{fig/freq-years}
+ \end{figure}
+ \end{minipage}%
+ \vspace{0.2cm}
+ \begin{minipage}{0.5\textwidth}
+ \textcolor{blue}{2)} \small \bf \textcolor{black}{Increasing the number of nodes}
+ \end{minipage}%
+ \begin{minipage}{0.6\textwidth}
+ \begin{figure}[h!]
+ \includegraphics[width=0.7\textwidth]{fig/clusters}
+ \end{figure}
+ \end{minipage}%
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 04 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Introduction and problem definition}
+ \bf \textcolor{blue}{Processor frequency and its energy consumption}
+ \vspace{0.4cm}
+ \begin{minipage}{0.5\textwidth}
+ \textcolor{blue}{$\blacktriangleright$}
+ \small \bf \textcolor{black}{ The power consumption of a processor increases exponentially when its
+ frequency is increased}
+ \end{minipage}%
+ \begin{minipage}{0.5\textwidth}
+ \begin{figure}[h!]
+ \includegraphics[width=0.7\textwidth]{fig/freq-power}
+ \end{figure}
+ \end{minipage}%
+
+ \begin{minipage}{0.5\textwidth}
+ \textcolor{blue}{$\blacktriangleright$}
+ \small \bf \textcolor{black}{The biggest power consumption is consumed by a processor in the computing node}
+
+ \end{minipage}%
+ \begin{minipage}{0.6\textwidth}
+ \begin{figure}[h!]
+ \includegraphics[width=0.9\textwidth]{fig/node-power}
+ \end{figure}
+ \end{minipage}%
+
+ \end{frame}
+
+ %%%%%%%%%%%%%%%%%%%
+%% SLIDE 05 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Introduction and problem definition}
+ \vspace{0.1cm}
+ \bf \textcolor{blue}{Techniques for energy consumption reduction}
+
+ \textcolor{blue}{1)} \bf \textcolor{black}{Switch-off idle nodes method}
+ \vspace{-0.9cm}
+ \begin{figure}
+ \animategraphics[autopause,loop,controls,scale=0.25,buttonsize=0.2cm]{200}{on-off/a-}{0}{69}
+ \end{figure}
+ \end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 06 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Techniques for energy consumption reduction}
+
+ \textcolor{blue}{2)} \bf \textcolor{black}{Dynamic voltage and frequency Scaling (DVFS)}
+ \vspace{-0.5cm}
+ \begin{figure}
+ \animategraphics[autopause,controls,scale=0.25,buttonsize=0.2cm]{10}{DVFS-meq/a-}{0}{109}
+ \end{figure}
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 07 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Using the energy reduction method}
+\section{\small {Using the energy reduction method}}
+\begin{block}{\textcolor{white}{Why we used DVFS method:}}
+\begin{itemize}
+ \item \textcolor{black}{It used to reduce the energy while keeping all node working, thus it is more conventional with parallel computing.}
+ \item \textcolor{black}{It has a very small overhead compared to switch-off idle nodes method.}
+ \end{itemize}
+\end{block}
+
+ \vspace{0.1cm}
+ \begin{block}{\textcolor{white}{Challenge and Objective}}
+
+ \textcolor{blue}{Challenge:} \textcolor{black}{DVFS is used to reduce the energy, \textcolor{blue}{but} it degrades the performance simultaneously.}
+
+ \vspace{0.1cm}
+ \textcolor{blue}{Objective:} \textcolor{black}{Optimizing both energy consumption and performance of a parallel application at the same time when DVFS is used.}
+\end{block}
+
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 08 %%
+%%%%%%%%%%%%%%%%%%%%
+
+
+\begin{frame}{Contributions}
+\section{\small {Contributions}}
+\subsection{\small {3.1 Energy optimization of homogeneous platform}}
+\begin{center}
+\bf \textcolor{black}{First contribution} \\
+\vspace{1cm}
+\bf \Large \textcolor{blue}{Energy optimization of homogeneous platform}
+\end{center}
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 09 %%
+%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}{Objectives}
+ \begin{femtoBlock}{} \vspace{-12 mm}
+ \begin{itemize} \small
+ \item Study the effect of the scaling factor $S$ on \textbf{energy consumption} of parallel iterative applications such as NAS
+ Benchmarks. \includegraphics[width=.06\textwidth]{c1/nasa.pdf} \medskip
+ \item Study the effect of the scaling factor $S$ on \textbf{performance} of these benchmarks.\medskip
+ \item Discovering the \textbf{energy-performance trade-off relation} when changing the frequency.\medskip
+ \item We propose an algorithm for selecting the scaling factor $S$ producing \textbf {optimal trade-off} between the energy and performance. \medskip
+ \item Improving Rauber and Rünger's\footnote{\tiny Thomas Rauber and Gudula Rünger. Analytical modeling and simulation of the
+ energy consumption \\ \quad ~ ~\quad of independent tasks. In Proceedings of the Winter Simulation Conference, 2012.} method that our method best on.
+ \end{itemize}
+ \let\thefootnote\relax\footnote{}
+ \vspace{-10 mm}
+ \end{femtoBlock}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 10 %%
+%%%%%%%%%%%%%%%%%%%%
+
+
+\begin{frame}{Parallel tasks execution over Homo. Platform}
+\vspace{-0.5 cm}
+\begin{figure}
+ \centering
+ \subfloat[Sync. imbalanced communications]{%
+ \includegraphics[scale=0.49]{c1/commtasks}\label{fig:h1}}
+ \subfloat[Sync. imbalanced computations]{%
+ \includegraphics[scale=0.49]{c1/compt}\label{fig:h2}}
+ \caption{Parallel tasks on homogeneous platform}
+ \label{fig:homo}
+\end{figure}
+
+ \end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 11 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Energy model for homogeneous platform}
+ The power consumed by a processor divided into two power metrics: the dynamic (\textcolor{red}{$P_d$}) and static
+ (\textcolor{red}{$P_s$}) power.
+ \begin{equation}
+ \label{eq:pd}
+ \textcolor{red}{ P_d} = \textcolor{blue}{\alpha \cdot CL \cdot V^2 \cdot F}
+ \end{equation}
+ \scriptsize \underline{Where}: \\
+ \scriptsize {\textcolor{blue}{$\alpha$}: switching activity \hspace{15 mm} \textcolor{blue}{$CL$}: load capacitance\\
+ \textcolor{blue}{$V$} the supply voltage \hspace{14 mm} \textcolor{blue}{$F$}: operational frequency}
+ \begin{equation}
+ \label{eq:ps}
+ \small \textcolor{red}{P_s} = \textcolor{blue}{V \cdot N_{trans} \cdot K_{design} \cdot I_{Leak}}
+ \end{equation}
+ \underline{Where}:\\
+ \scriptsize{ \textcolor{blue}{$V$}: the supply voltage. \hspace{28 mm} \textcolor{blue}{$N_{trans}$}: number of transistors. \\
+ \textcolor{blue}{$K_{design}$}: design dependent parameter. \hspace{8 mm} \textcolor{blue}{$I_{leak}$}: technology dependent
+ parameter.}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 12 %%
+%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}{Energy model for homogeneous platform}
+
+ The frequency scaling factor is the ratio between the maximum and the new frequency, \textcolor{blue}{$S = \frac{F_{max}}{F_{new}}$}. \medskip
+
+
+
+ \begin{block}{\small Rauber and Rünger's energy model}
+ $ E = P_{d} \cdot S_1^{-2} \cdot
+ \left( T_1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^2} \right) +
+ P_{s} \cdot S_1 \cdot T_1 \cdot N$
+ \end{block}
+ \textcolor{blue}{$S_1$}: the max. scaling factor\\
+ \textcolor{blue}{$P_{d}$}: the dynamic power\\
+ \textcolor{blue}{$P_{s}$}: the static power\\
+ \textcolor{blue}{$T_I$}: the time of the slower task\\
+ \textcolor{blue}{$T_i$}: the time of the other tasks\\
+ \textcolor{blue}{$N$}: the number of nodes
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 13 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Performance evaluation of MPI programs}
+ \begin{femtoBlock}{}
+ \vspace{-5 mm}
+ \begin{block}{\small Execution time prediction model}
+ \centering{ $ \textcolor{red}{T_{new}} = \textcolor{blue}{T_{Max Comp Old} \cdot S + T_{{Min Comm Old}}}$}
+ \end{block}
+ \vspace{10 mm}
+ \centering{\includegraphics[width=.4\textwidth]{c1/cg_per}
+ \quad%
+ \includegraphics[width=.4\textwidth]{c1/lu_pre}}
+ \vspace{5 mm}
+
+ \small The maximum normalized error for CG=0.0073 \textbf{(the smallest)} and LU=0.031 \textbf{(the worst)}.
+ \end{femtoBlock}
+\end{frame}
+
+
+
+
+ %%%%%%%%%%%%%%%%%%%%
+%% SLIDE 14 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Performance and energy reduction trade-off}
+ \begin{femtoBlock}{} \vspace{-15 mm}
+ \begin{figure}
+ \centering
+ \subfloat[\small Real relation.]{%
+ \includegraphics[width=.43\textwidth]{c1/file3}\label{fig:r2}}
+ \quad%
+ \subfloat[\small Converted relation.]{%
+ \includegraphics[width=.43\textwidth]{c1/file}\label{fig:r1}}%
+ \label{fig:rel}
+ % \caption{The energy and performance relation}
+\end{figure}
+
+ Where:~~~ $\textcolor{blue}{Performance} = execution~time^{-1}$
+
+%\vspace{-0.3cm}
+ \small
+ \begin{block}{\small Our objective function}
+ \centering{$\textbf{\emph {MaxDist}} = \max_{j=1,2,\dots ,F}
+ (\overbrace{P_{Norm}(S_j)}^{{Maximize}} -
+ \overbrace{E_{Norm}(S_j)}^{{Minimize}} )$}
+
+ \end{block}
+ \end{femtoBlock}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 15 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{Scaling factor selection algorithm}
+\vspace{-0.75cm}
+ \begin{center}
+ \includegraphics[width=.56 \textwidth]{c1/algo-homo}
+ \end{center}
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 16 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Scaling algorithm example}
+\vspace{-0.75cm}
+
+ \begin{figure}
+ \animategraphics[autopause,controls,scale=0.28,buttonsize=0.2cm]{10}{dvfs-homo/a-}{0}{159}
+
+ \end{figure}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 17 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Experimental results }
+ \begin{femtoBlock}{}
+ \begin{itemize}
+ \small
+ \item Our experiments are executed on the simulator SimGrid/SMPI v3.10.\medskip
+ \item Our algorithm is applied to NAS parallel benchmarks.\medskip
+ \item Each node in the cluster has 18 frequency values from \textbf{2.5$GHz$} to \textbf{800$MHz$}.\medskip
+ \item We run the classes A, B and C on 4, 8 or 9 and 16 nodes respectively.\medskip
+ \item The dynamic power with the highest frequency is equal to \textbf{20 $W$} and the power static is equal to \textbf{4 $W$}.
+ \end{itemize}
+ \end{femtoBlock}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 18 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Experimental results}
+ \begin{femtoBlock}{}
+ \centering {
+ \includegraphics[width=.35\textwidth]{c1/ep}
+ \includegraphics[width=.35\textwidth]{c1/cg}
+ \includegraphics[width=.35\textwidth]{c1/bt}}
+
+ \centering {\includegraphics[width=.55\textwidth]{c1/results.pdf}}
+ \end{femtoBlock}
+\end{frame}
+
+
+ %%%%%%%%%%%%%%%%%%%%
+%% SLIDE 19 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Results comparison}
+ \begin{block}{\small Rauber and Rünger's optimal scaling factor}
+ $S_{opt} = \sqrt[3]{\frac{2}{N} \cdot \frac{P_{dyn}}{P_{static}} \cdot
+ \left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3}\right) } $
+ \end{block}
+ \centering {
+ %\includegraphics[width=.33\textwidth]{c1/c1.pdf}
+ %\qquad
+ %\includegraphics[width=.33\textwidth]{c1/c2.pdf}}
+
+
+ \includegraphics[width=.55\textwidth]{c1/compare_c.pdf}}
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 20 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The proposed new energy model}
+ \vspace{-0.75cm}
+ \begin{figure}
+ \animategraphics[autopause,controls,scale=0.28,buttonsize=0.2cm]{10}{homo-model/a-}{0}{356}
+ \end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 21 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Comparing the new model with Rauber model }
+ \vspace{0.1cm}
+ \centering
+ \includegraphics[width=.45\textwidth]{c1/energy_con}
+
+ \includegraphics[width=.5\textwidth]{c1/compare-scales}
+\end{frame}
+
+
+
+
+ % \begin{frame}{Summary}
+ % \begin{femtoBlock}{}
+ % \begin{itemize}
+ %\small
+ %\item We have presented a new online scaling factor selection method that \textcolor{blue}{optimizes simultaneously the energy and performance}.\medskip
+ % \item It predicts \textcolor{blue}{ the energy consumption and the performance} of the parallel applications. \medskip
+ %\item Our algorithm \textcolor{blue}{saves more energy} when the communication and the other slacks times are big. \medskip
+ %\item It gives the \textcolor{blue}{best trade-off between energy reduction and
+ % performance}. \medskip
+ %\item Our method \ \textcolor{blue}{outperforms Rauber and Rünger's method} in terms of energy-performance ratio.
+ %\item The proposed new energy model is \textcolor{blue}{more accurate} then Rauber energy model.
+ %\end{itemize}
+
+ %\end{femtoBlock}
+%\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 22 %%
+%%%%%%%%%%%%%%%%%%%%
+
+
+\begin{frame}{Contribution}
+
+\subsection{\small {3.2 Energy optimization of heterogeneous platform}}
+\begin{center}
+\bf \textcolor{black}{Second contribution} \\
+\vspace{1cm}
+\bf \Large \textcolor{blue}{Energy optimization of Heterogeneous platform}
+\end{center}
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 23 %%
+%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}{Objectives}
+ \begin{femtoBlock}{} \vspace{-12 mm}
+ \begin{itemize} \small
+ \item Evaluating the \textcolor{blue}{new energy and performance models} of message passing applications with iterations running
+ over a heterogeneous platform (cluster and Grid). \medskip
+ \item Study the effect of the scaling factor $S$ on both \textcolor{blue}{energy consumption and the performance} of
+ message passing iterative applications. \medskip
+
+ \item Computing the vector of scaling factors ($S_1, S_2, ..., S_n$) producing \textcolor{blue} {optimal trade-off} between
+ energy consumption and performance.
+ \end{itemize}
+
+ \vspace{-10 mm}
+ \end{femtoBlock}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 24 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The execution time model}
+ \vspace{-8 mm}
+ \begin{figure}[!t]
+ \centering
+ \includegraphics[scale=0.5]{c2/commtasks}
+ \label{fig:heter}
+ \end{figure}
+ \vspace{-12 mm}
+ \medskip
+
+ \begin{block}{\small The execution time prediction model}
+ \begin{equation}
+ \label{eq:perf}
+ \small\textcolor{red}{ T_{new}} = \textcolor{blue}{\max_{i=1,2,\dots,N} ({TcpOld_i} \cdot S_{i}) + \min_{i=1,2,\dots,N} (Tcm_i)}
+ \end{equation}
+ \end{block}
+ \small Where: $ \textcolor{red}{Tcm} = \textcolor{blue}{communication~times + slack~times}$
+
+\end{frame}
+
+ %%%%%%%%%%%%%%%%%%%%
+%% SLIDE 25 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{The energy consumption model}
+ -The overall energy consumption of a message passing synchronous distributed application executed over a
+ heterogeneous platform is computed as follows:
+ \begin{multline}
+ \label{eq:energy}
+ \textcolor{red}{E} = \textcolor{blue}{\sum_{i=1}^{N} {(S_i^{-2} \cdot Pd_i \cdot Tcp_i)}} + {} \\
+ \textcolor{blue}{\sum_{i=1}^{N} (Ps_i \cdot (\max_{i=1,2,\dots,N} (Tcp_i \cdot S_{i}) + {\min_{i=1,2,\dots,N} (Tcm_i))}}
+ \hspace{10 mm}
+ \end{multline}
+ \underline{where}:\\
+ \textcolor{blue}{N} : is the number of nodes.
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 26 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{The energy model example for heter. cluster}
+ \vspace{-0.5cm}
+ \begin{figure}
+ \animategraphics[autopause,controls,scale=0.28,buttonsize=0.2cm]{10}{heter-model/a-}{0}{272}
+ \end{figure}
+ \end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 27 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The trade-off between energy and performance}
+ \vspace{-7 mm}
+ \begin{figure}
+ \centering{ \includegraphics[width=.4\textwidth]{c2/heter}}
+ \end{figure}
+ \vspace{-7 mm}
+ \textcolor{red}{\underline{Step1}}: computing the normalized energy \textcolor{blue}{$E_{norm} = \frac{E_{reduced}}
+ {E_{Max}}$}. \\
+ \textcolor{red}{\underline{Step2}}: computing the normalized performance \textcolor{blue}{$P_{norm} = \frac{T_{Max}}{T_{new}}$}.
+
+ \begin{block}{\small The tradeoff model}
+ \begin{equation}
+ \label{eq:max}
+ \textcolor{red}{MaxDist} =
+ \mathop {\max_{i=1,\dots F}}_{j=1,\dots,N}
+ (\overbrace{P_{norm}(S_{ij})}^{\text{\textcolor{blue}{Maximize}}} -
+ \overbrace{E_{norm}(S_{ij})}^{\text{\textcolor{blue}{Minimize}}} )
+ \end{equation}
+ \end{block}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 28 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{The scaling algorithm for heter. cluster}
+
+ \centering
+ \includegraphics[width=.52\textwidth]{algo-heter}
+ \end{frame}
+
+
+ %%%%%%%%%%%%%%%%%%%%
+%% SLIDE 29 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{The scaling algorithm example}
+ \vspace{-0.5cm}
+ \centering
+
+ \begin{figure}
+ \animategraphics[autopause,controls,scale=0.28,buttonsize=0.2cm]{10}{dvfs-heter/a-}{0}{650}
+ \end{figure}
+\end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 30 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Experiments over heterogeneous cluster }
+ \begin{itemize}
+ \small
+ \item The experiments executed on the simulator SimGrid/SMPI v3.10.\medskip
+ \item The scaling algorithm was applied to the NAS parallel benchmarks class C.\medskip
+ \item Four types of processors with different computing powers were used.\medskip
+ \item We ran the benchmarks on different number of nodes ranging from 4 to 144 nodes.\medskip
+ \item The total power consumption of the chosen CPUs is composed of $80\%$ for dynamic power and $20\%$ for static power.
+ \medskip
+
+ \end{itemize}
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 31 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The experimental results}
+ \vspace{-5 mm}
+ \begin{figure}[!t]
+ \centering
+ \includegraphics[width=0.8\textwidth]{c2/energy_saving.pdf}
+
+ \textcolor{blue}{On average, it saves the energy consumption by \textcolor{red}{29\%}
+ of NAS benchmarks class C executed over 8 nodes}
+
+ \end{figure}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 32 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The experimental results}
+ \vspace{-5 mm}
+ \begin{figure}[!t]
+ \centering
+
+ \includegraphics[width=.8\textwidth]{c2/perf_degra.pdf}
+
+ \textcolor{blue}{On average, it degrades the performance by \textcolor{red}{3.8\%}
+ of NAS benchmarks class C executed over 8 nodes}
+ \end{figure}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 33 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The results of the three powers scenarios}
+ \vspace{-5 mm}
+ \begin{figure}[!t]
+ \centering
+ \includegraphics[width=.55\textwidth]{c2/three_power.pdf}
+ \vspace{10 mm}
+ \includegraphics[width=.55\textwidth]{c2/three_scenarios.pdf}
+ \end{figure}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 34 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The comparing our method}
+ The proposed method (MaxDist) was compared to the EDP algorithm that minimizes the \textcolor{blue}{
+ $\mathit{energy}\times \mathit{delay}$} value.
+ \vspace{-5 mm}
+ \begin{figure}[!t]
+ \centering
+ \includegraphics[width=.55\textwidth]{c2/avg_compare.pdf}
+
+ \includegraphics[width=.55\textwidth]{c2/compare_with_EDP.pdf}
+ \end{figure}
+\end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 35 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Energy optimization of grid platform}
+ \begin{figure}[!t]
+ \centering
+ \includegraphics[width=.6\textwidth]{c2/grid5000.pdf}
+
+ \small 10 sites distributed over France and Luxembourg
+ \end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 36 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{Performance, Energy and trade-off models} \small
+ \begin{block}{\small The performance model of grid}
+ \begin{equation}
+ \label{eq:perf}
+ \Tnew = \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}({\TcpOld[ij]} \cdot S_{ij})
+ +\mathop{\min_{j=1,\dots,M_h}} (\Tcm[hj])
+\end{equation}
+ \end{block}
+
+
+ \begin{block}{\small The energy model of grid}\small
+ \begin{equation}
+ \label{eq:energy}
+ E = \sum_{i=1}^{N} \sum_{i=1}^{M_i} {(S_{ij}^{-2} \cdot \Pd[ij] \cdot \Tcp[ij])} +
+ \sum_{i=1}^{N} \sum_{j=1}^{M_i} (\Ps[ij] \cdot \Tnew)
+\end{equation}
+ \end{block}
+
+\begin{block}{\small The trade-off model of grid}
+\small
+ \begin{equation}
+ \label{eq:max}
+ \MaxDist =
+ \mathop{ \mathop{\max_{i=1,\dots N}}_{j=1,\dots,M_i}}_{k=1,\dots,F_j}
+ (\overbrace{\Pnorm(S_{ijk})}^{\text{Maximize}} -
+ \overbrace{\Enorm(S_{ijk})}^{\text{Minimize}} )
+\end{equation}
+ \end{block}
+
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 37 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{Experiments over Grid'5000}
+ \centering
+
+ \includegraphics[width=.5\textwidth]{c2/grid5000-2.pdf}
+
+ \vspace{-3 mm}
+ \textcolor{blue}{The experiments executed over one site and two sites scenarios}
+
+ \vspace{1mm}
+
+ \includegraphics[width=.5\textwidth]{c2/power_consumption.pdf}
+
+ \textcolor{blue}{We used Grid'5000 power measurement tools}
+\end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 38 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Experiments over Grid'5000}
+
+ \begin{minipage}{0.4\textwidth}
+ \textcolor{blue}{Execution the NAS class D on 16 nodes saves the energy by
+ \textcolor{red}{30\%}}
+ \end{minipage}
+ \begin{minipage}{0.55\textwidth}
+ \begin{figure}[h!]
+ \includegraphics[width=0.83 \textwidth]{c2/eng_s.eps}
+ \end{figure}
+\end{minipage}
+
+ \begin{minipage}{0.4\textwidth}
+ \textcolor{blue}{Execution the NAS class D on 16 nodes degrades the
+ performance by \textcolor{red}{3.2\%}}
+ \end{minipage}
+ \begin{minipage}{0.55\textwidth}
+ \begin{figure}[h!]
+ \includegraphics[width=.83\textwidth]{c2/per_d.eps}
+ \end{figure}
+ \end{minipage}
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 39 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Experiments over Grid'5000}
+ \textcolor{blue}{One core and Multi-cores per node results:}
+
+ \begin{figure}[h!]
+ \includegraphics[width=.48\textwidth]{c2/eng_s_mc.eps}
+ \hspace{0.3cm}
+ \includegraphics[width=.48\textwidth]{c2/per_d_mc.eps}
+ \end{figure}
+
+ \centering \small \textcolor{blue}{Using multi-core per node scenario decreases the computations to communications ratio}.
+\end{frame}
+
+
+
+%\begin{frame}{Summary}
+%\begin{itemize}
+ % \small
+ % \item Two scaling algorithm were applies to \textcolor{blue}{heterogeneous %cluster} and \textcolor{blue}{grid}.
+ % \item A new \textcolor{blue}{energy} and \textcolor{blue}{performance} models were proposed.
+ % \item The experimental results ere conducted over \textcolor{blue}{SimGrid} simulators and real
+ %test-bed \textcolor{blue}{Grid'5000}.
+
+ %\item The algorithm saves the energy by \textcolor{blue}{29\%} and only
+ % degrades the performance by \textcolor{blue}{3.8\%} for simulated heterogeneous
+ % clusters.
+
+ %\item The algorithm saves the energy by \textcolor{blue}{30\%} and only
+ % degrades the performance by \textcolor{blue}{3.2\%} for Grid'5000 results.
+
+ % \item The proposed method \textcolor{blue}{outperforms the EDP method} in terms of energy-performance ratio.
+ % \end{itemize}
+%\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 40 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Continuation}
+\subsection{\small {3.3 Energy optimization of asynchronous applications}}
+\begin{center}
+\bf \textcolor{black}{Third contribution} \\
+\vspace{1cm}
+\bf \Large \textcolor{blue}{Energy optimization of asynchronous applications}
+\end{center}
+ \end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 41 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Problem definition}\vspace{0.8 mm}
+\textcolor{blue}{Execution the parallel iterative application with synchronous communications }
+\vspace{-8 mm}
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.25,buttonsize=0.2cm]{10}{syn/a-}{0}{503}
+ \end{figure}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 42 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Problem definition}\vspace{0.8 mm}
+\textcolor{blue}{Execution the parallel iterative application with synchronous communications }
+\vspace{-8 mm}
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.25,buttonsize=0.2cm]{10}{asyn/a-}{0}{440}
+ \end{figure}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 43 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Solution}\vspace{0.8mm}
+\textcolor{blue}{Using asynchronous communications with DVFS }
+\vspace{-8 mm}
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.25,buttonsize=0.2cm]{10}{asyn+dvfs/a-}{0}{314}
+ \end{figure}
+\end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 44 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The performance models}
+
+\begin{block}{\small The performance model of Asynch. Applications}\small
+\begin{equation}
+ \label{eq:asyn_time}
+ \Tnew = \frac{\sum_{i=1}^{N} \sum_{j=1}^{M_i}({\TcpOld[ij]} \cdot S_{ij})} {N \cdot M_i }
+\end{equation}
+\end{block}
+
+
+\begin{block}{\small The performance model of Hybrid Applications}\small
+\begin{equation}
+ \label{eq:asyn_perf}
+ \Tnew = \frac{\sum_{i=1}^{N} (\max_{j=1,\dots, M_i} ({\TcpOld[ij]} \cdot S_{ij}) +
+ \min_{j=1,\dots,M_i} ({\Ltcm[ij]}))}{N}
+\end{equation}
+\end{block}
+
+
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 45 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The energy consumption models}
+
+\begin{block}{\small The energy model of Asynch. Applications}\small
+\begin{equation}
+ \label{eq:asyn_energy1}
+ E = \sum_{i=1}^{N} \sum_{j=1}^{M_i} {(S_{ij}^{-2} \cdot \Tcp[ij] \cdot (\Pd[ij]+\Ps[ij]) )}
+\end{equation}
+\end{block}
+
+
+\begin{block}{\small The energy model of Hybrid Applications}\small
+\begin{multline}
+ \label{eq:asyn_energy}
+ E = \sum_{i=1}^{N} \sum_{j=1}^{M_i} {(S_{ij}^{-2} \cdot \Pd[ij] \cdot \Tcp[ij])} + \sum_{i=1}^{N} \sum_{j=1}^{M_i} (\Ps[ij] \cdot \\
+ ( \mathop{\max_{j=1,\dots,M_i}} ({\Tcp[ij]} \cdot S_{ij}) + \mathop{\min_{j=1,\dots,M_i}} ({\Ltcm[ij]})))
+\end{multline}
+\end{block}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 46 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The scaling algorithm for Asynch. applications}
+\vspace{-0.1 mm}
+\centering
+\includegraphics[width=0.55\textwidth]{algo-hybrid.pdf}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 47 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The experimental results}
+ \vspace{-5 mm}
+ \begin{figure}[!t]
+ \centering
+ \includegraphics[width=0.5\textwidth]{c3/hybrid-model.pdf}
+ \end{figure}
+ \begin{itemize}
+ \small
+ \item Execution the iterative multi-splitting method over simulated Grid.
+ \item Execution the iterative multi-splitting method over Grid'5000 test-bed.
+ \end{itemize}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 48 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The simulation results}
+\centering \small \textcolor{blue}{The best scenario in term of energy and performance is the Async. MS with Sync. DVFS}
+
+\centering
+ \includegraphics[scale=0.46]{c3/energy_saving.eps}
+
+ \centering The average of energy saving = \textcolor{red}{22\%}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 49 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The simulation results}
+\centering
+
+ \includegraphics[scale=0.46]{c3/perf_degra.eps}
+
+ \centering The average of speed-up = \textcolor{red}{5.72\%}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 50 %%
+%%%%%%%%%%%%%%%%%%%%
+ \begin{frame}{The Grid'5000 results}
+ \vspace{-20 mm}
+ \begin{figure}[!t]
+ \centering
+ \hspace{-8 mm}
+ \includegraphics[width=0.53\textwidth]{c3/energy-s-compare.eps}
+ \includegraphics[width=0.53\textwidth]{c3/perf-deg-compare.eps}
+ \end{figure}
+ \vspace{-5 mm}
+ \centering
+ The energy saving = \textcolor{red}{26.93\%}, speeds up = \textcolor{red}{21.48\%}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 51 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{The comparison results}
+ \centering
+ \includegraphics[width=.5\textwidth]{c3/compare.eps}
+
+ \includegraphics[width=.5\textwidth]{c3/compare_scales.eps}
+\end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 52 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Conclusions}
+\section{Conclusions}
+\begin{itemize}
+
+\small \barrow We have proposed \textcolor{blue}{a new energy consumption and performance} models for
+ synchronous and asynchronous parallel applications with iterations.
+
+
+\small \barrow The parallel applications with iterations were executed over different parallel architectures such as: \textcolor{blue}{homogeneous cluster, heterogeneous cluster and
+grid}.
+
+\small \barrow We have proposed \textcolor{blue}{new objective function} to optimize both the energy consumption and the performance.
+
+\small \barrow \textcolor{blue}{New online frequency selecting algorithms} for clusters and grids were developed.
+
+\small \barrow The proposed algorithms were applied to the \textcolor{blue}{NAS parallel benchmarks} and \textcolor{blue}{the
+Multi-splitting} method.
+
+\small \barrow The proposed algorithms were evaluated over the \textcolor{blue}{SimGrid simulator and over Grid'5000 testbed}.
+
+\small \barrow All the proposed methods were compared with either \textcolor{blue}{Rauber and Rünger method} or \textcolor{blue}{EDP objective function}.
+
+
+\end{itemize}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 53 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Publication}
+
+\begin{block}{\small Journal Articles }\scriptsize
+\begin{enumerate}[$\lbrack$1$\rbrack$]
+
+\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier, Arnaud Giersch. Optimizing the energy consumption of message passing applications with iterations executed over grids. \textit{Journal of Computational
+ Science}, 2016.
+
+\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier, Arnaud Giersch. Energy Consumption Reduction for
+ Asynchronous Message Passing Applications. \textit{Journal of Supercomputing}, 2016, (Submitted)
+
+\end{enumerate}
+\end{block}
+
+
+\begin{block}{\small Conference Articles }\scriptsize
+
+\begin{enumerate}[$\lbrack$1$\rbrack$]
+
+\item Jean-Claude Charr, Raphaël Couturier, Ahmed Fanfakh, Arnaud Giersch. Dynamic Frequency Scaling for
+ Energy Consumption Reduction in Distributed MPI Programs. \textit{ISPA 2014}, pp.
+ 225-230. IEEE Computer Society, Milan, Italy (2014).
+
+\item Jean-Claude Charr, Raphaël Couturier, Ahmed Fanfakh, Arnaud Giersch. Energy Consumption Reduction
+ with DVFS for Message Passing Iterative Applications on Heterogeneous Architectures.
+ \textit{The $16^{th}$ PDSEC}. pp. 922-931. IEEE Computer Society, INDIA (2015).
+
+\item Ahmed Fanfakh, Jean-Claude Charr, Raphaël Couturier, Arnaud Giersch. CPUs Energy Consumption
+ Reduction for Asynchronous Parallel Methods Running over Grids. \textit{The $19^{th}$ CSE conference}. IEEE Computer Society,
+ Paris (2016).
+
+\end{enumerate}
+
+\end{block}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 54 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Perspectives}
+\section{Perspectives}
+
+\begin{itemize}
+
+\small \barrow We will adapt the proposed algorithms to take into consideration the
+\textcolor{blue}{variability between some iterations}.
+
+\small \barrow The proposed algorithms should be applied to \textcolor{blue}{other message passing methods with iterations} in order to see how they adapt to the characteristics of these methods.
+
+\small \barrow The proposed algorithms for heterogeneous platforms should be applied to heterogeneous platforms composed of \textcolor{blue}{CPUs and GPUs}.
+
+\small \barrow Comparing the results returned by the energy models to the values given by \textcolor{blue}{real instruments that measure the energy consumptions} of CPUs during the execution time.
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 55 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Fin} \vspace{-10 mm}
+
+ \centering \Large \textcolor{blue}{Thanks for Your Listening}
+
+ \vspace{2cm}
+ \centering \textcolor{blue}{ {\Large Questions?}}
+
+\end{frame}
+\end{document}
+% _____ ___ _ _
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+% | _| | || |\ |
+% |_| |___|_| \_|
+%
--- /dev/null
+\beamer@endinputifotherversion {3.33pt}
+\beamer@sectionintoc {1}{\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \topsep 3\p@ plus2\p@ minus2.5\p@ \parsep 0\p@ \itemsep 3\p@ plus2\p@ minus3\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip {Introduction and Problem definition}}{3}{0}{1}
+\beamer@sectionintoc {2}{\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \topsep 3\p@ plus2\p@ minus2.5\p@ \parsep 0\p@ \itemsep 3\p@ plus2\p@ minus3\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip {Using the energy reduction method}}{7}{0}{2}
+\beamer@sectionintoc {3}{\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \topsep 3\p@ plus2\p@ minus2.5\p@ \parsep 0\p@ \itemsep 3\p@ plus2\p@ minus3\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip {Contributions}}{8}{0}{3}
+\beamer@subsectionintoc {3}{1}{\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \topsep 3\p@ plus2\p@ minus2.5\p@ \parsep 0\p@ \itemsep 3\p@ plus2\p@ minus3\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip {3.1 Energy optimization of homogeneous platform}}{8}{0}{3}
+\beamer@subsectionintoc {3}{2}{\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \topsep 3\p@ plus2\p@ minus2.5\p@ \parsep 0\p@ \itemsep 3\p@ plus2\p@ minus3\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip {3.2 Energy optimization of heterogeneous platform}}{22}{0}{3}
+\beamer@subsectionintoc {3}{3}{\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \topsep 3\p@ plus2\p@ minus2.5\p@ \parsep 0\p@ \itemsep 3\p@ plus2\p@ minus3\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip {3.3 Energy optimization of asynchronous applications}}{40}{0}{3}
+\beamer@sectionintoc {4}{Conclusions}{52}{0}{4}
+\beamer@sectionintoc {5}{Perspectives}{54}{0}{5}
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--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=9
+ echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 10))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
+\documentclass{beamer}
+\usepackage{beamerthemefemto}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\DeclareGraphicsExtensions{.jpg, .png , .pdf, .bmp, .pdftex}
+\usepackage{algorithm,algorithmicx,algpseudocode}
+\usepackage{graphicx,graphics}
+\usepackage{subfig}
+\usepackage{listings}
+\usepackage{colortbl}
+\usepackage{amsmath}
+\usepackage{xspace}
+
+\usepackage[textsize=footnotesize]{todonotes}
+\title{Optimal Dynamic Frequency Scaling for Energy - Performance of Parallel MPI Programs}
+
+\author{Jean-Claude Charr, Raphaël Couturier, Ahmed Fanfakh
+ and Arnaud Giersch}
+\institute[DISC Department - AND Team]{FEMTO-ST - DISC Department - AND Team}
+\date{August 29th,~2014}
+% ____ _____ ____ _ _ _____
+% | _ \| ____| __ )| | | |_ _|
+% | | | | _| | _ \| | | | | |
+% | |_| | |___| |_) | |_| | | |
+% |____/|_____|____/ \___/ |_|
+%
+\begin{document}
+\setbeamertemplate{background}{\titrefemto}
+\begin{frame}[plain]
+\titlepage
+\end{frame}
+
+\setbeamertemplate{background}{\pagefemto}
+\begin{frame}{Outline}
+\setbeamertemplate{section in toc}[sections numbered]
+\tableofcontents
+\end{frame}
+\section{Definitions and objectives }
+\begin{frame}{Definitions}
+ \begin{femtoBlock}
+ {}
+% Et ici le texte dans le femtoBlock
+ \begin{itemize}
+ \small \item Modern processors provide \textbf{Dynamic Voltage and Frequency Scaling (DVFS)} technique. \medskip
+ \item DVFS is used to reduce the frequency and thus to \textbf{reduce the energy consumption} by a CPU while computing.\medskip
+ \item Energy consumption by \textbf{individual processor} of a synchronous parallel program:
+
+ $E_{ind} = P_{dyn} \cdot T_{Comp} + P_{static} \cdot (T_{Comp}+T_{Comm})$.\medskip
+ \item The frequency scaling factor is the ratio between the maximum and the new frequency, $S = \frac{F_{max}}{F_{new}}$. \medskip
+
+ \end{itemize}
+ \end{femtoBlock}
+\end{frame}
+
+
+\begin{frame}{Objectives}
+ \begin{femtoBlock}{} \vspace{-12 mm}
+ \begin{itemize} \small
+ \item Study the effect of the scaling factor $S$ on \textbf{energy consumption} of parallel iterative applications such as NAS
+ Benchmarks. \includegraphics[width=.06\textwidth]{fig/nasa.pdf} \medskip
+ \item Study the effect of the scaling factor $S$ on \textbf{performance} of these benchmarks.\medskip
+ \item Discovering the \textbf{energy-performance trade-off relation} when changing the frequency.\medskip
+ \item We propose an algorithm for selecting the scaling factor $S$ producing \textbf {optimal trade-off} between the energy and performance. \medskip
+ \item Improving Rauber and Rünger's\footnote{\tiny Thomas Rauber and Gudula Rünger. Analytical modeling and simulation of the
+ energy consumption \\ \quad ~ ~\quad of independent tasks. In Proceedings of the Winter Simulation Conference, 2012.} method that our method best on.
+ \end{itemize}
+ \let\thefootnote\relax\footnote{}
+ \vspace{-10 mm}
+ \end{femtoBlock}
+\end{frame}
+\section{Energy and performance models}
+\begin{frame}{Energy model for homogeneous platform}
+ \begin{femtoBlock}{}\small
+ The dynamic power is \textbf{exponentially} related to the scaling factor $S$ and the static consumed energy is \textbf{linearly}
+ related to this factor.
+ \begin{block}{\small Rauber and Rünger's energy model}
+ $ E = P_{dyn} \cdot S_1^{-2} \cdot
+ \left( T_1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^2} \right) +
+ P_{static} \cdot S_1 \cdot T_1 \cdot N$
+ \end{block}
+ $S_1$: is the max. scaling factor, $T_I$: is the time of the slower task, $T_i$: is the time of the other tasks and
+ $N$: is the number of nodes.
+ \begin{block}{\small Rauber and Rünger's optimal scaling factor}
+ $S_{opt} = \sqrt[3]{\frac{2}{N} \cdot \frac{P_{dyn}}{P_{static}} \cdot
+ \left( 1 + \sum_{i=2}^{N} \frac{T_i^3}{T_1^3}\right) } $
+ \end{block}
+ They reduce degradation of the performance by \textbf{setting the highest frequency to the slowest task}.
+ \end{femtoBlock}
+\end{frame}
+
+
+\begin{frame}{Performance evaluation of MPI programs}
+ \begin{femtoBlock}{}
+ \vspace{-5 mm}
+ \begin{block}{\small Execution time prediction model}
+ \centering{ $ T_{new} = T_{Max Comp Old} \cdot S + T_{{Max Comm Old}}$}
+ \end{block}
+ \vspace{10 mm}
+ \centering{\includegraphics[width=.35\textwidth]{fig/cg_per}
+ \quad%
+ \includegraphics[width=.35\textwidth]{fig/lu_pre}}
+ \vspace{5 mm}
+
+ \small The maximum normalized error for CG=0.0073 \textbf{(the smallest)} and LU=0.031 \textbf{(the worst)}.
+ \end{femtoBlock}
+\end{frame}
+
+\section{Performance and energy reduction trade-off}
+
+\begin{frame}{Performance and energy reduction trade-off}
+ \begin{femtoBlock}{} \vspace{-15 mm}
+ \begin{figure}
+ \centering
+ \subfloat[\small Real relation.]{%
+ \includegraphics[width=.4\textwidth]{fig/file3}\label{fig:r2}}
+ \quad%
+ \subfloat[\small Converted relation.]{%
+ \includegraphics[width=.4\textwidth]{fig/file}\label{fig:r1}}%
+ \label{fig:rel}
+ % \caption{The energy and performance relation}
+\end{figure}
+$Performance=\frac{1}{execution~time}$
+ \small
+ \begin{block}{\small Our objective function}
+ \centering{$\textbf{\emph {MaxDist}} = \max_{j=1,2,\dots ,F}
+ (\overbrace{P_{Norm}(S_j)}^{{Maximize}} -
+ \overbrace{E_{Norm}(S_j)}^{{Minimize}} )$}
+
+ \end{block}
+ \end{femtoBlock}
+
+\end{frame}
+
+
+
+
+\section{Experimental results and comparison}
+
+\begin{frame}{Experimental results }
+ \begin{femtoBlock}{}
+ \begin{itemize}
+ \small
+ \item Our experiments are executed on the simulator SimGrid/SMPI v3.10.\medskip
+ \item Our algorithm is applied to NAS parallel benchmarks.\medskip
+ \item Each node in the cluster has 18 frequency values from \textbf{2.5$GHz$} to \textbf{800$MHz$}.\medskip
+ \item We run the classes A, B and C on 4, 8 or 9 and 16 nodes respectively.\medskip
+ \item The dynamic power with the highest frequency is equal to \textbf{20 $W$} and the power static is equal to \textbf{4 $W$}.
+ \end{itemize}
+ \end{femtoBlock}
+\end{frame}
+
+\begin{frame}{Experimental results}
+ \begin{femtoBlock}{}
+ \centering {
+ \includegraphics[width=.35\textwidth]{fig/ep}
+ \includegraphics[width=.35\textwidth]{fig/cg}
+ \includegraphics[width=.35\textwidth]{fig/bt}}
+
+ \centering {\includegraphics[width=.55\textwidth]{fig/results.pdf}}
+ \end{femtoBlock}
+\end{frame}
+
+\begin{frame}{Results comparison}
+ \begin{femtoBlock}{}
+ \centering {
+ \includegraphics[width=.33\textwidth]{fig/c1.pdf}
+ \qquad
+ \includegraphics[width=.33\textwidth]{fig/c2.pdf}}
+
+
+ \includegraphics[width=.45\textwidth]{fig/compare_c.pdf}
+ \end{femtoBlock}
+\end{frame}
+
+
+
+
+
+\section{Conclusions}
+\begin{frame}{Conclusions}
+ \begin{femtoBlock}{}
+ \begin{itemize}
+ \small
+ \item We have presented a new online scaling factor selection method that \textbf{optimizes simultaneously the energy and performance}.\medskip
+ \item It predicts \textbf{ the energy consumption and the performance} of the parallel applications. \medskip
+ \item Our algorithm \textbf{saves more energy} when the communication and the other slacks times are big. \medskip
+ \item It gives the \textbf{best trade-off between energy reduction and
+ performance}. \medskip
+ \item Our method \textbf{outperforms Rauber and Rünger's method} in terms of energy-performance ratio.
+ \end{itemize}
+
+ \end{femtoBlock}
+\end{frame}
+
+
+
+
+\begin{frame}{Thanks for Listening} \vspace{-10 mm}
+ \begin{femtoBlock}{}
+ \begin{block}{\small Appeared}
+ This work has appeared in ISPA conference proceedings, 26-28 August 2014
+ \end{block}
+\medskip
+\medskip \medskip \medskip
+
+
+ \centering {\Large Questions?}
+
+ \end{femtoBlock}
+\end{frame}
+
+\end{document}
+% _____ ___ _ _
+% | ___|_ _| \ | |
+% | |_ | || \| |
+% | _| | || |\ |
+% |_| |___|_| \_|
+%
--- /dev/null
+\begin{frame}{DVFS technique}
+\vspace{-8 mm}
+
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.28,buttonsize=0.2cm]{10}{DVFS-meq/a-}{0}{109}
+
+ \end{figure}
+\end{frame}
+
+
+
+
+\begin{frame}{On-OFF scheduling technique }
+\vspace{-8 mm}
+
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.27,buttonsize=0.2cm]{200}{on-off/a-}{0}{69}
+
+ \end{figure}
+\end{frame}
+
+
+\begin{frame}{The scaling algorithm on homogeneous cluster}
+\vspace{-8 mm}
+
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{dvfs-homo/a-}{0}{159}
+
+ \end{figure}
+\end{frame}
+
+\begin{frame}{The scaling algorithm for heterogeneous cluster}
+\vspace{-8 mm}
+
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{dvfs-heter/a-}{0}{650}
+ \end{figure}
+\end{frame}
+
+
+\begin{frame}{The scaling algorithm for asynchronous applications}
+\vspace{-8 mm}
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{syn/a-}{0}{503}
+ \end{figure}
+\end{frame}
+
+
+\begin{frame}{The scaling algorithm for asynchronous applications}
+\vspace{-8 mm}
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{asyn/a-}{0}{440}
+ \end{figure}
+\end{frame}
+
+\begin{frame}{The scaling algorithm for asynchronous applications}
+\vspace{-8 mm}
+\begin{figure}
+ \animategraphics[autopause,controls,scale=0.26,buttonsize=0.2cm]{10}{asyn+dvfs/a-}{0}{314}
+ \end{figure}
+\end{frame}
+
+
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--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=20
+ echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 21))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
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--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=20
+ echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 21))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
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+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
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+ x="522.13715"
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+ </g>
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+ <flowRoot
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+ id="flowRoot5159"
+ style="fill:black;stroke:none;stroke-opacity:1;stroke-width:1px;stroke-linejoin:miter;stroke-linecap:butt;fill-opacity:1;font-family:Sans;font-style:normal;font-weight:bold;font-size:14px;line-height:125%;letter-spacing:0px;word-spacing:0px;-inkscape-font-specification:Sans Bold"><flowRegion
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+ xml:space="preserve"
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ style="fill:#000080">Computing</flowPara></flowRoot> <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:role="line"
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+ sodipodi:role="line"
+ x="650.70825"
+ y="824.55292"
+ id="tspan5179"
+ style="fill:#000080">A to finish</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:linespacing="125%"
+ transform="translate(18,355.27146)"><tspan
+ sodipodi:role="line"
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+ sodipodi:role="line"
+ x="647.30737"
+ y="883.50214"
+ id="tspan5185">with A</tspan></text>
+ <flowRoot
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ style="fill:#ff0000">Case 2</flowPara></flowRoot> <text
+ xml:space="preserve"
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+ sodipodi:role="line"
+ x="15.870934"
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+ style="fill:#0000ff">comunications</tspan></text>
+ </g>
+ </g>
+ <g
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+ <rect
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+ </g>
+ <flowRoot
+ xml:space="preserve"
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:role="line"
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+ sodipodi:role="line"
+ x="35.14278"
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+ </g>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:role="line"
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+ y="912.36151"
+ id="tspan4923-3">Total idle times</tspan></text>
+ </g>
+ </g>
+</svg>
--- /dev/null
+%-------------------------------------------------------------------------------
+% LaTeX Beamer theme "femto" from the femto-st evaluation model (2011) JM Nicod and PC Heam (LIFC)
+%
+% author: Christophe Varnier et passage au ".sty" par G. Laurent
+% Joel Abadie (12/06/2012) rajout de fonctionnalites tikzpicture
+% Jean-Marc Nicod (logo + reglage pied de page)
+%-------------------------------------------------------------------------------
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{beamerthemefemto}[2012/06/05 beamer theme femto package]
+\RequirePackage{times}
+\RequirePackage{tikz}
+%-------------------------------------------------------------------------------
+
+% _ _ _ _
+% ___| |_ _ _| | ___ ___| |_ ___ ___ _ _| | ___ _ _ _ __ ___
+% / __| __| | | | |/ _ \ / _ \ __| / __/ _ \| | | | |/ _ \ | | | '__/ __|
+% \__ \ |_| |_| | | __/ | __/ |_ | (_| (_) | |_| | | __/ |_| | | \__ \
+% |___/\__|\__, |_|\___| \___|\__| \___\___/ \__,_|_|\___|\__,_|_| |___/
+% |___/
+%
+
+% commande permettant de dessiner une page de fond
+% appel depuis le document par : \setbeamertemplate{background}{\titrefemto}
+\newcommand{\titrefemto}{
+\begin{tikzpicture}
+ %definition du node centre au dimension de la page
+ \node[minimum height=\paperheight, minimum width=\paperwidth](centre) {};
+ % placement des logos en bas à gauche
+ \matrix[above right=4mm, ampersand replacement=\&] at (centre.south west){
+ \node[anchor=center]{\includegraphics[width=7mm]{logo-UFC.jpg}}; \&
+ \node[anchor=center]{\includegraphics[width=6mm]{logo-CNRS.jpg}}; \&
+ \node[anchor=center]{\includegraphics[width=13mm]{logo-ENSMM.jpg}}; \&
+ \node[anchor=center]{\includegraphics[width=12mm]{logo-UTBM.jpg}}; \\
+ };
+ %placement des logos en haut à droite
+ \node[below left, inner sep=0] at (centre.north east) {\includegraphics[width=5.5cm]{Hexagones.jpg}};
+ %placement des logos en haut à gauche
+% \node[below right=6mm] at (centre.north west) {\includegraphics[width=2.8cm]{Femto-logo_couleur-2012.png}};
+ \node[below right=6mm] at (centre.north west) {\includegraphics[width=2.8cm]{logo-FEMTO.jpg}};
+\end{tikzpicture}
+}
+
+% commande permettant de dessiner une page de fond
+% appel depuis le document par : \setbeamertemplate{background}{\pagefemto}
+\newcommand{\pagefemto}{
+\begin{tikzpicture}
+ % definition du node centre au dimension de la page
+ \node[minimum height=\paperheight, minimum width=\paperwidth](centre) {};
+ % placement des logos en bas à gauche
+% \node[above right=3mm] at (centre.south west) {\includegraphics[width=1.2cm]{Femto-logo_couleur-2012.png}};
+ \node[above right=0.75mm] at ([shift={(0.25,0)}]centre.south west) {\includegraphics[width=1.2cm]{logo-FEMTO.jpg}};
+ %placement des logos en haut à droite
+ \node[below left, inner sep=0](hexa) at (centre.north east) {\includegraphics[width=3.9cm]{Hexagones.jpg}};
+ %trace des traits
+ \coordinate (A) at ([shift={(0.5,-1.4)}]centre.north west);
+ \coordinate (B) at (A-| hexa.west);
+ \draw[BleuFemtoTitre] (A) -- ([xshift=-3mm]B);
+ %trait inferieur
+% \coordinate (A) at ([shift={(0.5,1.1)}]centre.south west);
+ \coordinate (A) at ([shift={(0.5,.8)}]centre.south west);
+% \coordinate (B) at ([shift={(-0.5,1.1)}]centre.south east);
+ \coordinate (B) at ([shift={(-0.5,.8)}]centre.south east);
+ \draw[BleuFemtoTitre] (A) -- (B);
+\end{tikzpicture}
+}
+
+% \definecolor{GreenYellow}{cmyk}{0.15,0,0.69,0} % PANTONE 388
+% \definecolor{Yellow}{cmyk}{0,0,1.,0} % PANTONE YELLOW
+% \definecolor{Goldenrod}{cmyk}{0,0.10,0.84,0} % PANTONE 109
+% \definecolor{Dandelion}{cmyk}{0,0.29,0.84,0} % PANTONE 123
+% \definecolor{Apricot}{cmyk}{0,0.32,0.52,0} % PANTONE 1565
+% \definecolor{Peach}{cmyk}{0,0.50,0.70,0} % PANTONE 164
+% \definecolor{Melon}{cmyk}{0,0.46,0.50,0} % PANTONE 177
+% \definecolor{YellowOrange}{cmyk}{0,0.42,1.,0} % PANTONE 130
+% \definecolor{Orange}{cmyk}{0,0.61,0.87,0} % PANTONE ORANGE-021
+% \definecolor{BurntOrange}{cmyk}{0,0.51,1.,0} % PANTONE 388
+% \definecolor{Bittersweet}{cmyk}{0,0.75,1.,0.24} % PANTONE 167
+% \definecolor{RedOrange}{cmyk}{0,0.77,0.87,0} % PANTONE 179
+% \definecolor{Mahogany}{cmyk}{0,0.85,0.87,0.35} % PANTONE 484
+% \definecolor{Maroon}{cmyk}{0,0.87,0.68,0.32} % PANTONE 201
+% \definecolor{BrickRed}{cmyk}{0,0.89,0.94,0.28} % PANTONE 1805
+% \definecolor{Red}{cmyk}{0,1.,1.,0} % PANTONE RED
+% \definecolor{OrangeRed}{cmyk}{0,1.,0.50,0} % No PANTONE,match
+% \definecolor{RubineRed}{cmyk}{0,1.,0.13,0} % PANTONE RUBINE-RED
+% \definecolor{WildStrawberry}{cmyk}{0,0.96,0.39,0} % PANTONE 206
+% \definecolor{Salmon}{cmyk}{0,0.53,0.38,0} % PANTONE 183
+% \definecolor{CarnationPink}{cmyk}{0,0.63,0,0} % PANTONE 218
+% \definecolor{Magenta}{cmyk}{0,1.,0,0} % PANTONE PROCESS-MAGENTA
+% \definecolor{VioletRed}{cmyk}{0,0.81,0,0} % PANTONE 219
+% \definecolor{Rhodamine}{cmyk}{0,0.82,0,0} % PANTONE RHODAMINE-RED
+% \definecolor{Mulberry}{cmyk}{0.34,0.90,0,0.02} % PANTONE 241
+% \definecolor{RedViolet}{cmyk}{0.07,0.90,0,0.34} % PANTONE 234
+% \definecolor{Fuchsia}{cmyk}{0.47,0.91,0,0.08} % PANTONE 248
+% \definecolor{Lavender}{cmyk}{0,0.48,0,0} % PANTONE 223
+% \definecolor{Thistle}{cmyk}{0.12,0.59,0,0} % PANTONE 245
+% \definecolor{Orchid}{cmyk}{0.32,0.64,0,0} % PANTONE 252
+% \definecolor{DarkOrchid}{cmyk}{0.40,0.80,0.20,0} % No PANTONE match
+% \definecolor{Purple}{cmyk}{0.45,0.86,0,0} % PANTONE PURPLE
+% \definecolor{Plum}{cmyk}{0.50,1.,0,0} % PANTONE 518
+% \definecolor{Violet}{cmyk}{0.79,0.88,0,0} % PANTONE VIOLET
+% \definecolor{RoyalPurple}{cmyk}{0.75,0.90,0,0} % PANTONE 267
+% \definecolor{BlueViolet}{cmyk}{0.86,0.91,0,0.04} % PANTONE 2755
+% \definecolor{Periwinkle}{cmyk}{0.57,0.55,0,0} % PANTONE 2715
+% \definecolor{CadetBlue}{cmyk}{0.62,0.57,0.23,0} % PANTONE (534+535)
+% \definecolor{CornflowerBlue}{cmyk}{0.65,0.13,0,0} % PANTONE 292
+% \definecolor{MidnightBlue}{cmyk}{0.98,0.13,0,0.43} % PANTONE 302
+% \definecolor{NavyBlue}{cmyk}{0.94,0.54,0,0} % PANTONE 293
+% \definecolor{RoyalBlue}{cmyk}{1.,0.50,0,0} % No PANTONE match
+% \definecolor{Blue}{cmyk}{1.,1.,0,0} % PANTONE BLUE-072
+% \definecolor{Cerulean}{cmyk}{0.94,0.11,0,0} % PANTONE 3005
+% \definecolor{Cyan}{cmyk}{1.,0,0,0} % PANTONE PROCESS-CYAN
+% \definecolor{ProcessBlue}{cmyk}{0.96,0,0,0} % PANTONE PROCESS-BLUE
+% \definecolor{SkyBlue}{cmyk}{0.62,0,0.12,0} % PANTONE 2985
+% \definecolor{Turquoise}{cmyk}{0.85,0,0.20,0} % PANTONE (312+313)
+% \definecolor{TealBlue}{cmyk}{0.86,0,0.34,0.02} % PANTONE 3145
+% \definecolor{Aquamarine}{cmyk}{0.82,0,0.30,0} % PANTONE 3135
+% \definecolor{BlueGreen}{cmyk}{0.85,0,0.33,0} % PANTONE 320
+% \definecolor{Emerald}{cmyk}{1.,0,0.50,0} % No PANTONE match
+% \definecolor{JungleGreen}{cmyk}{0.99,0,0.52,0} % PANTONE 328
+% \definecolor{SeaGreen}{cmyk}{0.69,0,0.50,0} % PANTONE 3268
+% \definecolor{Green}{cmyk}{1.,0,1.,0} % PANTONE GREEN
+% \definecolor{ForestGreen}{cmyk}{0.91,0,0.88,0.12} % PANTONE 349
+% \definecolor{PineGreen}{cmyk}{0.92,0,0.59,0.25} % PANTONE 323
+% \definecolor{LimeGreen}{cmyk}{0.50,0,1.,0} % No PANTONE match
+% \definecolor{YellowGreen}{cmyk}{0.44,0,0.74,0} % PANTONE 375
+% \definecolor{SpringGreen}{cmyk}{0.26,0,0.76,0} % PANTONE 381
+% \definecolor{OliveGreen}{cmyk}{0.64,0,0.95,0.40} % PANTONE 582
+% \definecolor{RawSienna}{cmyk}{0,0.72,1.,0.45} % PANTONE 154
+% \definecolor{Sepia}{cmyk}{0,0.83,1.,0.70} % PANTONE 161
+% \definecolor{Brown}{cmyk}{0,0.81,1.,0.60} % PANTONE 1615
+% \definecolor{Tan}{cmyk}{0.14,0.42,0.56,0} % No PANTONE match
+% \definecolor{Gray}{cmyk}{0,0,0,0.50} % PANTONE COOL-GRAY-8
+\definecolor{DarkGray}{cmyk}{0,0,0,0.80} % PANTONE COOL-GRAY-8
+% \definecolor{Black}{cmyk}{0,0,0,1.} % PANTONE PROCESS-BLACK
+% \definecolor{White}{cmyk}{0,0,0,0} % No PANTONE match
+
+% ajout des couleurs Femto
+\definecolor{BleuFemtoTitre}{cmyk}{0.94,0.83,0,0.01}
+\definecolor{BleuFemtoTexte}{cmyk}{0.92,0.54,0.05,0.09}
+\definecolor{BleuFemto}{RGB}{39,84,148}
+\definecolor{BleuClairFemto}{RGB}{66,153,214}
+\definecolor{VertFemto}{RGB}{175,203,81}
+\definecolor{GrisClairFemto}{RGB}{177,179,180}
+\definecolor{GrisFemto}{RGB}{112,127,135}
+
+\usetheme{default}
+
+\setbeamertemplate{navigation symbols}{}
+
+\setbeamercolor{structure}{fg=DarkGray}
+
+% _ _ _ _ _ _
+%| |_ ___ _ __ ___ _ __ | | __ _| |_ ___ | |_(_) |_ _ __ ___
+%| __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \ | __| | __| '__/ _ \
+%| || __/ | | | | | |_) | | (_| | || __/ | |_| | |_| | | __/
+% \__\___|_| |_| |_| .__/|_|\__,_|\__\___| \__|_|\__|_| \___|
+% |_|
+
+%\pgfdeclareimage[height=\paperheight,width=\paperwidth]{titrefemto}{TitreFemto.png}
+
+\setbeamertemplate{title page}
+{
+\vskip 10mm
+\usebeamerfont{title}\usebeamercolor[fg]{title}\LARGE\textcolor{BleuFemto}\inserttitle
+\newline\newline
+\normalsize\textcolor{GrisFemto}\insertauthor
+\newline
+\vskip 1mm
+\textcolor{GrisFemto}\insertinstitute
+\newline\newline
+\footnotesize\textcolor{GrisFemto}\insertdate
+}
+
+% _ _ _
+%| |_ ___ _ __ ___ _ __ | | __ _| |_ ___ _ __ __ _ __ _ ___
+%| __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \ | '_ \ / _` |/ _` |/ _ \
+%| || __/ | | | | | |_) | | (_| | || __/ | |_) | (_| | (_| | __/
+% \__\___|_| |_| |_| .__/|_|\__,_|\__\___| | .__/ \__,_|\__, |\___|
+% |_| |_| |___/
+
+%\pgfdeclareimage[height=\paperheight,width=\paperwidth]{pagefemto}{PageFemto.png}
+
+\setbeamertemplate{frametitle}{\vspace{6mm}\hspace{-5mm}\Large\bf\textcolor{BleuFemto} \insertframetitle}
+
+% pour les block
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--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=20
+ echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 21))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
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--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=9
+ echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 10))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
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--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=20
+ echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 21))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
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+ style="fill:#008000"> 15.2</tspan> + <tspan
+ style="fill:#008080"
+ id="tspan6251"> 8.1</tspan> = <tspan
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+ style="fill:#ff0000">23.3 Joule</tspan></tspan></text>
+ <text
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:role="line"
+ id="tspan4912-0"
+ x="42.57143"
+ y="981.86151"> 25*(1.40) * 0.35+</tspan></text>
+ <text
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+ y="972.36157"
+ x="140"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="972.36157"
+ x="140"
+ id="tspan4983-6-9"
+ sodipodi:role="line"> -2</tspan></text>
+ </g>
+ <g
+ id="g5076-6-7"
+ transform="translate(14,49.99992)"
+ style="fill:#008000">
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:linespacing="125%"><tspan
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+ sodipodi:role="line"
+ id="tspan4912-0-2"
+ x="42.57143"
+ y="979.86151"> 30*(1.88) * 0.25</tspan></text>
+ <text
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+ id="text4981-7-2-5"
+ y="970.36157"
+ x="120"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="970.36157"
+ x="120"
+ id="tspan4983-6-9-4"
+ sodipodi:role="line"> -2</tspan></text>
+ </g>
+ <flowRoot
+ transform="translate(-4,355.27146)"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ xml:space="preserve"><flowRegion
+ id="flowRegion5184"><rect
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+ id="flowPara5188"
+ style="fill:#008080"> 4 * 0.541 + </flowPara><flowPara
+ id="flowPara4264">+<flowSpan
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+ id="flowSpan4266"> 5 * 0.541 +</flowSpan></flowPara><flowPara
+ id="flowPara4290"
+ style="fill:#008080"> 6 * 0.541</flowPara><flowPara
+ id="flowPara4274"
+ style="fill:#008080"> </flowPara></flowRoot> <flowRoot
+ xml:space="preserve"
+ id="flowRoot6149"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ id="flowPara6155">E=</flowPara></flowRoot> <text
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+ style="font-size:59.23067474px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ y="566.32861">{</tspan></text>
+ <text
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+ style="font-size:59.23067474px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ transform="scale(0.54825599,1.8239655)"><tspan
+ sodipodi:role="line"
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+ x="506.03442"
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+ <text
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:role="line"
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+ x="333.35034"
+ y="637.49103"> </tspan></text>
+ <text
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+ id="text5178-0"
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+ x="757.67114"
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+ xml:space="preserve"><tspan
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+ x="757.67114"
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+ </g>
+ </g>
+ </g>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ id="text3810-9-59"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
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+ id="tspan5491"><tspan
+ id="tspan5548"
+ style="font-size:18px;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 2: </tspan><tspan
+ style="fill:#0000ff"
+ id="tspan5497">S1=1.08, S2=1.40, S3=1.88</tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ x="-700"
+ y="512.36151"
+ id="text3810-9-59-6"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan3812-9-40-8"
+ x="-700"
+ y="512.36151"
+ style="font-size:18px;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 2:</tspan><tspan
+ sodipodi:role="line"
+ x="-700"
+ y="532.86804"
+ style="font-size:16px"
+ id="tspan5491-8">Computing frequency scaling factor S<tspan
+ style="fill:#0000ff"
+ id="tspan3217">i</tspan>=Fmax<tspan
+ style="fill:#0000ff"
+ id="tspan3219">i</tspan> / Fnew<tspan
+ style="fill:#0000ff"
+ id="tspan3221">i</tspan><tspan
+ style="fill:#ff0000"
+ id="tspan5495-4"> e.g</tspan><tspan
+ style="fill:#0000ff"
+ id="tspan5497-3"> S1=2.5/2.3 =1.08 </tspan></tspan><tspan
+ sodipodi:role="line"
+ x="-700"
+ y="552.86804"
+ style="font-size:16px;fill:#0000ff"
+ id="tspan3211"> S2=2.8/2.0 =1.40</tspan><tspan
+ sodipodi:role="line"
+ x="-700"
+ y="572.86804"
+ style="font-size:16px;fill:#0000ff"
+ id="tspan3215"> S3=3.4/1.8 =1.88</tspan></text>
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+ <text
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
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+ <text
+ transform="translate(0,355.27146)"
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ x="308.57144"
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+ id="text5625"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan5627"
+ x="308.57144"
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+ style="fill:#550000"> 0.541 0.491 0.473</tspan></text>
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+ sodipodi:linespacing="125%"
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+ y="409.94717"
+ x="681.42859"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="409.94717"
+ x="681.42859"
+ id="tspan5650"
+ sodipodi:role="line" /><tspan
+ style="fill:#ff0000"
+ y="427.44717"
+ x="681.42859"
+ id="tspan5652"
+ sodipodi:role="line">MAX</tspan></text>
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+ style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;marker-end:url(#Arrow1Mend-5)" />
+ </g>
+ </g>
+ </g>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan3812-9-4-6-4"
+ x="28"
+ y="764.36151"
+ style="font-size:18px;font-style:normal;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 4:</tspan><tspan
+ sodipodi:role="line"
+ x="28"
+ y="784.86804"
+ style="font-size:16px;font-style:normal;fill:#0000ff;-inkscape-font-specification:Sans Bold"
+ id="tspan5577-1"><tspan
+ id="tspan5876-4"
+ style="font-size:16px;font-style:normal;fill:#000000;-inkscape-font-specification:Sans Bold">Computing the enenrgy consumption of all nodes </tspan></tspan><tspan
+ sodipodi:role="line"
+ x="28"
+ y="804.86804"
+ style="font-size:16px;font-style:normal;fill:#0000ff;-inkscape-font-specification:Sans Bold"
+ id="tspan5929"><tspan
+ style="font-size:16px;font-style:normal;fill:#000000;-inkscape-font-specification:Sans Bold"
+ id="tspan5931">E=<tspan
+ style="fill:#008000"
+ id="tspan5933">Sum of all dynamic Energies </tspan>+ <tspan
+ style="fill:#008080"
+ id="tspan5939">Sum of all static Energies </tspan></tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:13.99994469px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan5978"
+ x="30"
+ y="862.36151"
+ style="fill:#0000ff">where: </tspan><tspan
+ sodipodi:role="line"
+ x="30"
+ y="879.86145"
+ id="tspan5980">Pd1 = 20W Pd2=25 Pd3=30</tspan><tspan
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+ x="30"
+ y="897.36139"
+ id="tspan5982">Ps1 = 4W Ps2=5 Ps3=6</tspan></text>
+ <flowRoot
+ xml:space="preserve"
+ id="flowRoot6231"
+ style="fill:black;stroke:none;stroke-opacity:1;stroke-width:1px;stroke-linejoin:miter;stroke-linecap:butt;fill-opacity:1;font-family:Sans;font-style:normal;font-weight:bold;font-size:14px;line-height:125%;letter-spacing:0px;word-spacing:0px;-inkscape-font-specification:Sans Bold"><flowRegion
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+ id="flowPara6237" /></flowRoot> <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ x="1007.1221"
+ y="332.42496"
+ style="fill:#550000"></tspan><tspan
+ sodipodi:role="line"
+ x="1007.1221"
+ y="349.92496"
+ style="fill:#550000"
+ id="tspan4013" /></text>
+ <text
+ xml:space="preserve"
+ style="font-size:65.00091553%;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;baseline-shift:super;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ y="-7.9964495"
+ id="text4027"
+ sodipodi:linespacing="125%"
+ transform="translate(0,355.27146)"><tspan
+ sodipodi:role="line"
+ id="tspan4029"
+ x="773.77686"
+ y="-7.9964495">huuiio</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ x="752.56366"
+ y="-12.03706"
+ id="text4031"
+ sodipodi:linespacing="125%"
+ transform="translate(0,355.27146)"><tspan
+ sodipodi:role="line"
+ id="tspan4033"
+ x="752.56366"
+ y="-12.03706" /></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ y="341.51633"
+ id="text4035"
+ sodipodi:linespacing="125%"
+ transform="translate(0,355.27146)"><tspan
+ sodipodi:role="line"
+ id="tspan4037"
+ x="515.1778"
+ y="341.51633" /></text>
+ <g
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+ transform="translate(744.18793,-12.177734)">
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
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+ x="36"
+ y="700.36151"
+ style="font-size:18px;font-style:normal;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 3:</tspan><tspan
+ sodipodi:role="line"
+ x="36"
+ y="720.86804"
+ style="font-size:16px;font-style:normal;fill:#0000ff;-inkscape-font-specification:Sans Bold"
+ id="tspan5577"><tspan
+ id="tspan5876"
+ style="font-size:16px;font-style:normal;fill:#000000;-inkscape-font-specification:Sans Bold">Computing the new execution time </tspan> Tnew=Max ((Tcp . S )) + Min(Tcp ) <tspan
+ style="fill:#550000"
+ id="tspan5878">=0.541 </tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#0000ff;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:linespacing="125%"><tspan
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+ x="508.18793"
+ y="728.18378"><tspan
+ style="font-style:italic;-inkscape-font-specification:Sans Bold Italic"
+ id="tspan4085"> i </tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:italic;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#0000ff;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold Italic"
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+ y="728.36151"
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+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
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+ x="542"
+ y="728.36151"> i</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:italic;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#0000ff;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold Italic"
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+ id="text4039-3-8"
+ sodipodi:linespacing="125%"><tspan
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--- /dev/null
+#!/bin/bash
+
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+ i=0
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+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 21))
+ #echo "$i $j"
+
+ done
+
+
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ <text
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+ style="font-size:18px;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 1:</tspan><tspan
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+ style="font-size:12px;font-style:normal;font-weight:bold;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:role="line"
+ id="tspan4912-0"
+ x="42.57143"
+ y="981.86151"> 20*(1.38) * 0.50+</tspan></text>
+ <text
+ sodipodi:linespacing="125%"
+ id="text4981-7-2"
+ y="972.36157"
+ x="140"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
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+ xml:space="preserve"><tspan
+ y="671.37573"
+ x="140"
+ id="tspan5135"
+ sodipodi:role="line"> </tspan></text>
+ <g
+ id="g5076-6-7"
+ transform="translate(14,49.99992)"
+ style="fill:#008000">
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ sodipodi:role="line"
+ id="tspan4912-0-2"
+ x="42.57143"
+ y="979.86151"> 20*(1.38) * 0.50</tspan></text>
+ <text
+ sodipodi:linespacing="125%"
+ id="text4981-7-2-5"
+ y="970.36157"
+ x="120"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#008000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
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+ id="tspan4983-6-9-4"
+ sodipodi:role="line"> -2</tspan></text>
+ </g>
+ <text
+ transform="scale(0.58414358,1.7119079)"
+ sodipodi:linespacing="125%"
+ id="text5178"
+ y="603.04736"
+ x="390.31506"
+ style="font-size:63.09572601px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="603.04736"
+ x="390.31506"
+ id="tspan5180"
+ sodipodi:role="line">}</tspan></text>
+ <flowRoot
+ transform="translate(0,355.27146)"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ id="flowRoot5182"
+ xml:space="preserve"><flowRegion
+ id="flowRegion5184"><rect
+ y="634.23291"
+ x="261.42856"
+ height="42.857117"
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+ id="flowPara5188">+ <flowSpan
+ style="fill:#008080"
+ id="flowSpan6239">4 * 0.6920 * 3 </flowSpan></flowPara></flowRoot> <text
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+ id="text5190"
+ y="649.94714"
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+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="649.94714"
+ x="361.42856"
+ id="tspan5192"
+ sodipodi:role="line" /></text>
+ <text
+ transform="translate(0,355.27146)"
+ sodipodi:linespacing="125%"
+ id="text5198"
+ y="642.80432"
+ x="430"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="642.80432"
+ x="430"
+ id="tspan5200"
+ sodipodi:role="line" /></text>
+ <flowRoot
+ xml:space="preserve"
+ id="flowRoot6149"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ width="32.857143"
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+ id="flowPara6155">E=</flowPara></flowRoot> <g
+ id="g6255"
+ transform="translate(0,2)">
+ <text
+ sodipodi:linespacing="125%"
+ id="text6157"
+ y="1068.6472"
+ x="10.571426"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="1068.6472"
+ x="10.571426"
+ id="tspan6159"
+ sodipodi:role="line">= </tspan></text>
+ <text
+ sodipodi:linespacing="125%"
+ id="text6241"
+ y="1070.5875"
+ x="84.008926"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="1070.5875"
+ x="84.008926"
+ id="tspan6243"
+ sodipodi:role="line"><tspan
+ id="tspan6249"
+ style="fill:#008000"> 33</tspan> + <tspan
+ id="tspan6251"
+ style="fill:#008080">8.304</tspan> = <tspan
+ id="tspan6253"
+ style="fill:#ff0000">41.304 Joule</tspan></tspan></text>
+ <text
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+ sodipodi:linespacing="125%"
+ id="text6245"
+ y="621.37573"
+ x="397.14285"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="621.37573"
+ x="397.14285"
+ id="tspan6247"
+ sodipodi:role="line"> </tspan></text>
+ </g>
+ </g>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ x="36"
+ y="670.36151"
+ id="text3810-9-59"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ x="36"
+ y="670.36151"
+ style="font-size:16px"
+ id="tspan5491"><tspan
+ id="tspan5548"
+ style="font-size:18px;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 2: </tspan><tspan
+ style="fill:#0000ff"
+ id="tspan5497">S=1.38</tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ x="-119.99999"
+ y="264.36148"
+ id="text3810-9-59-6"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan3812-9-40-8"
+ x="-119.99999"
+ y="264.36148"
+ style="font-size:18px;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 2:</tspan><tspan
+ sodipodi:role="line"
+ x="-119.99999"
+ y="284.86798"
+ style="font-size:16px"
+ id="tspan5491-8">Computing frequency scaling factor S=Fmax / Fnew <tspan
+ style="fill:#ff0000"
+ id="tspan5495-4">e.g</tspan><tspan
+ style="fill:#0000ff"
+ id="tspan5497-3"> S=2.5/1.8 =1.38</tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ x="36"
+ y="700.36151"
+ id="text3810-9-3-3"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan3812-9-4-6"
+ x="36"
+ y="700.36151"
+ style="font-size:18px;font-style:normal;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 3:</tspan><tspan
+ sodipodi:role="line"
+ x="36"
+ y="720.86804"
+ style="font-size:16px;font-style:normal;fill:#0000ff;-inkscape-font-specification:Sans Bold"
+ id="tspan5577"><tspan
+ id="tspan5876"
+ style="font-size:16px;font-style:normal;fill:#000000;-inkscape-font-specification:Sans Bold">Computing the new execution time </tspan> Tnew=max ((Tcp.S) . Tcm) <tspan
+ style="fill:#550000"
+ id="tspan5878">=0.6920</tspan></tspan></text>
+ <g
+ id="g5863"
+ transform="translate(531.42856,-50)">
+ <path
+ inkscape:connector-curvature="0"
+ id="path5600"
+ d="m 302,694.36149 440,0"
+ style="fill:#008000;stroke:#1b4e14;stroke-width:3;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
+ <text
+ sodipodi:linespacing="125%"
+ id="text5602"
+ y="720.36151"
+ x="301.71429"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="720.36151"
+ x="301.71429"
+ id="tspan5604"
+ sodipodi:role="line">0.5*1.38+0.001 0.5*1.38+0.0015 0.50*1.38+0.002</tspan></text>
+ <text
+ transform="translate(0,355.27146)"
+ sodipodi:linespacing="125%"
+ id="text5625"
+ y="387.09003"
+ x="308.57144"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ style="fill:#550000"
+ y="387.09003"
+ x="308.57144"
+ id="tspan5627"
+ sodipodi:role="line"> 0.6910 0.6915 0.6920</tspan></text>
+ <text
+ transform="translate(0,355.27146)"
+ sodipodi:linespacing="125%"
+ id="text5648"
+ y="409.94717"
+ x="681.42859"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ xml:space="preserve"><tspan
+ y="409.94717"
+ x="681.42859"
+ id="tspan5650"
+ sodipodi:role="line" /><tspan
+ style="fill:#ff0000"
+ y="427.44717"
+ x="681.42859"
+ id="tspan5652"
+ sodipodi:role="line">MAX</tspan></text>
+ <path
+ inkscape:connector-curvature="0"
+ id="path5654"
+ d="m 700,770.36149 0,-20"
+ style="fill:none;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;marker-end:url(#Arrow1Mend-5)" />
+ </g>
+ <text
+ xml:space="preserve"
+ style="font-size:14px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
+ x="34"
+ y="746.36151"
+ id="text3810-9-3-3-2"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan3812-9-4-6-4"
+ x="34"
+ y="746.36151"
+ style="font-size:18px;font-style:normal;font-weight:bold;fill:#ff0000;-inkscape-font-specification:Sans Bold">Step 4:</tspan><tspan
+ sodipodi:role="line"
+ x="34"
+ y="766.86804"
+ style="font-size:16px;font-style:normal;fill:#0000ff;-inkscape-font-specification:Sans Bold"
+ id="tspan5577-1"><tspan
+ id="tspan5876-4"
+ style="font-size:16px;font-style:normal;fill:#000000;-inkscape-font-specification:Sans Bold">Computing the enenrgy consumption of all nodes </tspan></tspan><tspan
+ sodipodi:role="line"
+ x="34"
+ y="786.86804"
+ style="font-size:16px;font-style:normal;fill:#0000ff;-inkscape-font-specification:Sans Bold"
+ id="tspan5929"><tspan
+ style="font-size:16px;font-style:normal;fill:#000000;-inkscape-font-specification:Sans Bold"
+ id="tspan5931">E=<tspan
+ style="fill:#008000"
+ id="tspan5933">Sum of all dynamic Energies </tspan>+ <tspan
+ style="fill:#008080"
+ id="tspan5939">Sum of all static Energies </tspan></tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:13.99994469px;font-style:normal;font-weight:bold;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans;-inkscape-font-specification:Sans Bold"
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+ y="832.36151"
+ id="text5976"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan5978"
+ x="20"
+ y="832.36151"
+ style="fill:#0000ff">where: </tspan><tspan
+ sodipodi:role="line"
+ x="20"
+ y="849.86145"
+ id="tspan5980">Pd = 20W</tspan><tspan
+ sodipodi:role="line"
+ x="20"
+ y="867.36139"
+ id="tspan5982">Ps = 4W</tspan></text>
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+ id="flowRoot6231"
+ style="fill:black;stroke:none;stroke-opacity:1;stroke-width:1px;stroke-linejoin:miter;stroke-linecap:butt;fill-opacity:1;font-family:Sans;font-style:normal;font-weight:bold;font-size:14px;line-height:125%;letter-spacing:0px;word-spacing:0px;-inkscape-font-specification:Sans Bold"><flowRegion
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+</svg>
--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=9
+ # echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 10))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
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--- /dev/null
+#!/bin/bash
+
+#for f in {9..11}; do cp aa/a-3.png a-$f.png; done
+#for f in {$i..$j}; do cp ${file} a-$f.png; done
+ i=0
+ j=20
+ echo "$i $j"
+FILES="aa/*"
+ for file in $FILES
+ do
+ for f in $(seq $i $j)
+ do
+ cp ${file} a-$f.png
+ c=1
+ done
+ #echo ${file}
+ i=$(($j + 1))
+ j=$(($j + 21))
+ #echo "$i $j"
+
+ done
+
+
--- /dev/null
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