X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy.git/blobdiff_plain/b039491f5ad738be1d313f6203bec5d1d39a84e8..7d2b5d8b8dc27be4b702a3c63174abdd62dd6670:/paper.tex?ds=sidebyside

diff --git a/paper.tex b/paper.tex
index e6d6745..2ec1b17 100644
--- a/paper.tex
+++ b/paper.tex
@@ -1,33 +1,31 @@
 \documentclass[12pt]{article}
 %\documentclass[12pt,twocolumn]{article}
-\DeclareMathSizes{40}{4000}{200}{2000}
+
 \usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
 \usepackage[english]{babel}
 \usepackage{algorithm,algorithmicx,algpseudocode}
 \usepackage{graphicx,graphics}
 \usepackage{subfig}
 \usepackage{listings}
 \usepackage{colortbl}
-\usepackage{sectsty}
-\usepackage{titlesec}
-\usepackage{secdot}
+% \usepackage{sectsty}
+% \usepackage{titlesec}
+% \usepackage{secdot}
 %\usepackage[font={footnotesize,bt}]{caption}
 %\usepackage[font=scriptsize,labelfont=bf]{caption}
+\usepackage{lmodern}
+
+\usepackage{todonotes}
+\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\small\textbf{AG:} #2}}
 
 \begin{document}
-\begin{center}
-  \Large
-  \title*\textbf{Optimal Dynamic Frequency Scaling for Energy-Performance of Parallel MPI Programs}
-\end{center}
-\parskip 0pt
-\linespread{1.18}
-\normalsize
-\makeatletter
-\renewcommand*{\@seccntformat}[1]{\csname the#1\endcsname\hspace{0.01cm}}
-\makeatother
-\sectionfont{\large}
-
-\section{.~Introduction }
+
+\title{Optimal Dynamic Frequency Scaling for Energy-Performance of Parallel MPI Programs}
+\author{A. Badri \and J.-C. Charr \and R. Couturier \and A. Giersch}
+\maketitle
+
+\section{Introduction}
 
 The need for computing power is still increasing and it is not expected to slow
 down in the coming years. To satisfy this demand, researchers and supercomputers
@@ -69,15 +67,13 @@ using the simulator Simgrid/SMPI v3.10~\cite{45} over an homogeneous distributed
 memory architecture. Furthermore, we compare the proposed algorithm with
 Rauber's methods. The comparison's results show that our algorithm gives better
 energy-time trade off.
-\sectionfont{\large}
 
-\section{.~Related Works }
+\section{Related Works}
 
 In the this section some heuristics, to compute the scaling factor, are
 presented and classified in two parts : offline and online methods.
- \sectionfont{\large}
 
-\subsection{~The offline DVFS orientations}
+\subsection{The offline DVFS orientations}
 
 The DVFS offline methods are static and are not executed during the runtime of
 the program. Some approaches used heuristics to select the best DVFS state
@@ -92,9 +88,8 @@ algorithm, while in~\cite{38,34}, Cochran et al. used multi logistic regression
 algorithm for the same goal. The offline study that shown the DVFS impact on the
 communication time of the MPI program is~\cite{17}, Freeh et al. show that these
 times not changed when the frequency is scaled down.
-\sectionfont{\large}
 
-\subsection{~The online DVFS orientations}
+\subsection{The online DVFS orientations}
 
 The objective of these works is to dynamically compute and set the frequency of
 the CPU during the runtime of the program for saving energy. Estimating and
@@ -128,9 +123,8 @@ paper.  However, the primary contributions of this paper are:
 \item The proposed algorithm works online without profiling or training as
   in~\cite{38,34}.
 \end{enumerate}
-\sectionfont{\large}
 
-\section{.~Parallel Tasks Execution on Homogeneous Platform}
+\section{Parallel Tasks Execution on Homogeneous Platform}
 
 A homogeneous cluster consists of identical nodes in terms of the hardware and
 the software. Each node has its own memory and at least one processor which can
@@ -158,9 +152,8 @@ of the program is the execution time of the slowest task as :
   Program Time=MAX_{i=1,2,..,N} (T_i) \hfill
 \end{equation}
 where $T_i$ is the execution time of process $i$.
-\sectionfont{\large}
 
-\section{.~Energy Model for Homogeneous Platform}
+\section{Energy Model for Homogeneous Platform}
 
 The energy consumption by the processor consists of two powers metric: the
 dynamic and the static power. This general power formulation is used by many
@@ -196,7 +189,7 @@ maximum and the new frequency as in EQ~(\ref{eq:s}).
   S=\:\frac{F_{max}}{F_{new}} \hfill  \newline
 \end{equation}
 The value of the scale \emph S is grater than 1 when changing the frequency to
-any new frequency value(\emph {P-state}) in governor.~It is equal to 1 when the
+any new frequency value(\emph {P-state}) in governor. It is equal to 1 when the
 frequency are set to the maximum frequency.  The energy consumption model for
 parallel homogeneous platform is depending on the scaling factor \emph S. This
 factor reduces quadratically the dynamic power.  Also, this factor increases the
@@ -232,9 +225,8 @@ scaling factor as in EQ~(\ref{eq:sopt}).
   S_{opt}= {\sqrt [3~]{\frac{2}{n} \frac{P_{dyn}}{P_{static}}  \Big(1+\sum\limits_{i=2}^{N}\frac{T_i^3}{T_1^3}\Big) }} \hfill
 \end{equation}
 %[\Big 3]
-\sectionfont{\large}
 
-\section{.~Performance Evaluation of MPI Programs}
+\section{Performance Evaluation of MPI Programs}
 
 The performance (execution time) of the parallel MPI applications are depends on
 the time of the slowest task as in figure~(\ref{fig:homo}). Normally the
@@ -272,9 +264,8 @@ paper we predict the execution time of the program for any new scaling factor
 value. Depending on this prediction we can produce our energy-performace scaling
 method as we will show in the coming sections. In the next section we make an
 investigation study for the EQ~(\ref{eq:tnew}).
-\sectionfont{\large}
 
-\section{.~Performance Prediction Verification }
+\section{Performance Prediction Verification}
 
 In this section we evaluate the precision of our performance prediction methods
 on the NAS benchmark. We use the EQ~(\ref{eq:tnew}) that predicts the execution
@@ -303,9 +294,8 @@ and SP. The average normalized errors between the predicted execution time and
 the real time (Simgrid time) for all programs is between 0.0032 to 0.0133. AS an
 example, we are present the execution times of the NAS benchmarks as in the
 figure~(\ref{fig:pred}).
-\sectionfont{\large}
 
-\section{.~Performance to Energy Competition}
+\section{Performance to Energy Competition}
 This section demonstrates our approach for choosing the optimal scaling
 factor. This factor gives maximum energy reduction taking into account the
 execution time for both computation and communication times . The relation
@@ -364,17 +354,15 @@ optimal way when the energy function has a convex form with frequency scaling
 factor as shown in ~\cite{15,3,19}. Energy measurement model is not the
 objective of this paper and we choose Rauber's model as an example with two
 reasons that mentioned before.
-\sectionfont{\large}
 
-\section{.~Optimal Scaling Factor for Performance and Energy }
+\section{Optimal Scaling Factor for Performance and Energy}
 
 In the previous section we described the objective function that satisfy our
 goal in discovering optimal scaling factor for both performance and energy at
 the same time. Therefore, we develop an energy to performance scaling algorithm
 (EPSA). This algorithm is simple and has a direct way to calculate the optimal
-scaling factor for both energy and performance at the same time.  \clearpage
-\linespread{1}
-\begin{algorithm}[width=\textwidth,height=\textheight,keepaspectratio]
+scaling factor for both energy and performance at the same time.
+\begin{algorithm}[t]
   \caption{EPSA}
   \label{EPSA}
   \begin{algorithmic}[1]
@@ -400,18 +388,19 @@ scaling factor for both energy and performance at the same time.  \clearpage
     \State  $ Return \; \;  (S_{optimal})$
   \end{algorithmic}
 \end{algorithm}
-\linespread{1.2} The proposed EPSA algorithm works online during the execution
-time of the MPI program. It selects the optimal scaling factor by gathering some
-information from the program after one iteration. This algorithm has small
-execution time (between 0.00152 $ms$ for 4 nodes to 0.00665 $ms$ for 32
-nodes). The data required by this algorithm is the computation time and the
-communication time for each task from the first iteration only. When these times
-are measured, the MPI program calls the EPSA algorithm to choose the new
-frequency using the optimal scaling factor. Then the program set the new
-frequency to the system. The algorithm is called just one time during the
-execution of the program. The following example shows where and when the EPSA
-algorithm is called in the MPI program : \clearpage
-\begin{lstlisting}
+The proposed EPSA algorithm works online during the execution time of the MPI
+program. It selects the optimal scaling factor by gathering some information
+from the program after one iteration. This algorithm has small execution time
+(between 0.00152 $ms$ for 4 nodes to 0.00665 $ms$ for 32 nodes). The data
+required by this algorithm is the computation time and the communication time
+for each task from the first iteration only. When these times are measured, the
+MPI program calls the EPSA algorithm to choose the new frequency using the
+optimal scaling factor. Then the program set the new frequency to the
+system. The algorithm is called just one time during the execution of the
+program. The following example shows where and when the EPSA algorithm is called
+in the MPI program :
+\begin{minipage}{\textwidth}
+\begin{lstlisting}[frame=tb]
 FOR J:=1 to Some_iterations Do
    -Computations Section.
    -Communications Section.
@@ -424,6 +413,7 @@ FOR J:=1 to Some_iterations Do
    ENDIF
 ENDFOR
 \end{lstlisting}
+\end{minipage}
 After obtaining the optimal scale factor from the EPSA algorithm. The program
 calculates the new frequency $F_i$ for each task proportionally to its time
 value $T_i$. By substitution of the EQ~(\ref{eq:s}) in the EQ~(\ref{eq:si}), we
@@ -435,9 +425,8 @@ According to this equation all the nodes may have the same frequency value if
 they have balanced workloads. Otherwise, they take different frequencies when
 have imbalanced workloads. Then EQ~(\ref{eq:fi}) works in adaptive way to change
 the freguency according to the nodes workloads.
-\sectionfont{\large}
 
-\section{.~Experimental Results}
+\section{Experimental Results}
 
 The proposed ESPA algorithm was applied to seven MPI programs of the NAS
 benchmarks (EP ,CG , MG ,FT , BT, LU and SP). We work on three classes (A, B and
@@ -495,7 +484,6 @@ same time over all available scales.
   \caption{Optimal scaling factors for The NAS MPI Programs}
   \label{fig:nas}
 \end{figure}
-\linespread{1.1}
 \begin{table}[width=\textwidth,height=\textheight,keepaspectratio]
   \caption{Optimal Scaling Factors Results}
   % title of Table
@@ -515,7 +503,6 @@ same time over all available scales.
   \label{table:factors results}
   % is used to refer this table in the text
 \end{table}
-\linespread{1.2}
 
 As shown in the table~(\ref{table:factors results}), when the optimal scaling
 factor has big value we can gain more energy savings for example as in CG and
@@ -525,10 +512,7 @@ communication and the other slacks times are big and smaller ones in opposite
 cases. In EP there are no communications inside the iterations. This make our
 EPSA to selects smaller scaling factor values (inducing smaller energy savings).
 
-% \clearpage
-\sectionfont{\large}
-
-\section{.~Comparing Results}
+\section{Comparing Results}
 
 In this section, we compare our EPSA algorithm results with Rauber's
 methods~\cite{3}. He had two scenarios, the first is to reduce energy to optimal
@@ -540,7 +524,6 @@ scenario as $Rauber_{E-P}$. The comparison is made in tables~(\ref{table:compare
   Class A},\ref{table:compare Class B},\ref{table:compare Class C}). These
 tables show the results of our EPSA and Rauber's two scenarios for all the NAS
 benchmarks programs for classes A,B and C.
-%\linespread{1}
 \begin{table}[ht]
   \caption{Comparing Results for  The NAS Class A}
   % title of Table
@@ -665,17 +648,16 @@ benchmarks programs for classes A,B and C.
 \label{table:compare Class C}
 % is used to refer this table in the text
 \end{table}
-%\linespread{1.2}
-\clearpage As shown in these tables our scaling factor is not optimal for energy
-saving such as Rauber's scaling factor EQ~(\ref{eq:sopt}), but it is optimal for
-both the energy and the performance simultaneously. Our EPSA optimal scaling
-factors has better simultaneous optimization for both the energy and the
-performance compared to Rauber's energy-performance method
-($Rauber_{E-P}$). Also, in ($Rauber_{E-P}$) method when setting the frequency to
-maximum value for the slower task lead to a small improvement of the
-performance. Also the results show that this method keep or improve energy
-saving. Because of the energy consumption decrease when the execution time
-decreased while the frequency value increased.
+As shown in these tables our scaling factor is not optimal for energy saving
+such as Rauber's scaling factor EQ~(\ref{eq:sopt}), but it is optimal for both
+the energy and the performance simultaneously. Our EPSA optimal scaling factors
+has better simultaneous optimization for both the energy and the performance
+compared to Rauber's energy-performance method ($Rauber_{E-P}$). Also, in
+($Rauber_{E-P}$) method when setting the frequency to maximum value for the
+slower task lead to a small improvement of the performance. Also the results
+show that this method keep or improve energy saving. Because of the energy
+consumption decrease when the execution time decreased while the frequency value
+increased.
 
 Figure~(\ref{fig:compare}) shows the maximum distance between the energy saving
 percent and the performance degradation percent. Therefore, this means it is the
@@ -697,7 +679,6 @@ than the first.
   \label{fig:compare}
 \end{figure}
 
-\clearpage
 \bibliographystyle{plain}
 \bibliography{my_reference}
 \end{document}
