X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/mpi-energy.git/blobdiff_plain/c00a8e3e79d7a39860d4c701f85adff1cc02788b..b950ac52c83730085568b6bf91ac498a5fed2030:/paper.tex?ds=inline

diff --git a/paper.tex b/paper.tex
index babc12b..962a22b 100644
--- a/paper.tex
+++ b/paper.tex
@@ -14,8 +14,9 @@
 % \usepackage{secdot}
 %\usepackage[font={footnotesize,bt}]{caption}
 %\usepackage[font=scriptsize,labelfont=bf]{caption}
-\usepackage{todonotes}
-\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\small\textbf{AG:} #2}}
+\usepackage{xspace}
+\usepackage[textsize=footnotesize]{todonotes}
+\newcommand{\AG}[2][inline]{\todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}
 
 \begin{document}
 
@@ -36,18 +37,20 @@
 
 \maketitle
 
-\AG{``Optimal'' is a bit pretentious in the title}
+\AG{``Optimal'' is a bit pretentious in the title.\\
+  Complete affiliation, add an email address, etc.}
 
 \begin{abstract}
   \AG{complete the abstract\dots}
 \end{abstract}
 
 \section{Introduction}
+\label{sec.intro}
 
 The need for computing power is still increasing and it is not expected to slow
 down in the coming years. To satisfy this demand, researchers and supercomputers
 constructors have been regularly increasing the number of computing cores in
-supercomputers (for example in November 2013, according to the top 500
+supercomputers (for example in November 2013, according to the TOP500
 list~\cite{43}, the Tianhe-2 was the fastest supercomputer. It has more than 3
 millions of cores and delivers more than 33 Tflop/s while consuming 17808
 kW). This large increase in number of computing cores has led to large energy
@@ -82,10 +85,22 @@ this algorithm to seven MPI benchmarks. These MPI programs are the NAS parallel
 benchmarks (NPB v3.3) developed by NASA~\cite{44}. Our experiments are executed
 using the simulator SimGrid/SMPI v3.10~\cite{Casanova:2008:SGF:1397760.1398183}
 over an homogeneous distributed memory architecture. Furthermore, we compare the
-proposed algorithm with Rauber's methods. The comparison's results show that our
+proposed algorithm with Rauber's methods.
+\AG{Add citation for Rauber's methods.  Moreover, Rauber was not alone to to this work (use ``Rauber et al.'', or ``Rauber and Gudula'', or \dots)}
+The comparison's results show that our
 algorithm gives better energy-time trade off.
+%
+\AG{Correctly reword the following}%
+In Section~\ref{sec.relwork} we present works from other
+authors. Then, in Sections~\ref{sec.ptasks} and~\ref{sec.energy}, we
+introduce our model. [\dots] Finally, we conclude in
+Section~\ref{sec.concl}.
 
 \section{Related Works}
+\label{sec.relwork}
+
+\AG{Consider introducing the models (sec.~\ref{sec.ptasks},
+  maybe~\ref{sec.energy}) before related works}
 
 In the this section some heuristics, to compute the scaling factor, are
 presented and classified in two parts : offline and online methods.
@@ -95,7 +110,9 @@ presented and classified in two parts : offline and online methods.
 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
 during the compilation phases as an example in Azevedo et al.~\cite{40}. He used
-intra-task algorithm to choose the DVFS setting when there are dependency points
+intra-task algorithm
+\AG{what is an ``intra-task algorithm''?}
+to choose the DVFS setting when there are dependency points
 between tasks. While in~\cite{29}, Xie et al. used breadth-first search
 algorithm to do that. Their goal is saving energy with time limits. Another
 approaches gathers and stores the runtime information for each DVFS state, then
@@ -142,6 +159,7 @@ paper.  However, the primary contributions of this paper are:
 \end{enumerate}
 
 \section{Parallel Tasks Execution on Homogeneous Platform}
+\label{sec.ptasks}
 
 A homogeneous cluster consists of identical nodes in terms of the hardware and
 the software. Each node has its own memory and at least one processor which can
@@ -151,11 +169,13 @@ we consider execution of the synchronous tasks on distributed homogeneous
 platform. These tasks can exchange the data via synchronous memory passing.
 \begin{figure*}[t]
   \centering
-  \subfloat[Synch. Imbalanced Communications]{\includegraphics[scale=0.67]{synch_tasks}\label{fig:h1}}
-  \subfloat[Synch. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
+  \subfloat[Sync. Imbalanced Communications]{\includegraphics[scale=0.67]{synch_tasks}\label{fig:h1}}
+  \subfloat[Sync. Imbalanced Computations]{\includegraphics[scale=0.67]{compt}\label{fig:h2}}
   \caption{Parallel Tasks on Homogeneous Platform}
   \label{fig:homo}
 \end{figure*}
+\AG{On fig.~\ref{fig:h1}, how can there be a synchronization point without communications just before ?\\
+Use ``Sync.'' to abbreviate ``Synchronization''}
 Therefore, the execution time of a task consists of the computation time and the
 communication time. Moreover, the synchronous communications between tasks can
 lead to idle time while tasks wait at the synchronous point for others tasks to
@@ -172,6 +192,7 @@ of the program is the execution time of the slowest task as :
 where $T_i$ is the execution time of process $i$.
 
 \section{Energy Model for Homogeneous Platform}
+\label{sec.energy}
 
 The energy consumption by the processor consists of two powers metric: the
 dynamic and the static power. This general power formulation is used by many
@@ -180,38 +201,40 @@ $P_{dyn}$ is related to the switching activity $\alpha$, load capacitance $C_L$,
 the supply voltage $V$ and operational frequency $f$ respectively as follow :
 \begin{equation}
   \label{eq:pd}
-  P_{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
+ \textit P_{dyn} = \alpha \cdot C_L \cdot V^2 \cdot f
 \end{equation}
 The static power $P_{static}$ captures the leakage power consumption as well as
 the power consumption of peripheral devices like the I/O subsystem.
 \begin{equation}
   \label{eq:ps}
-  P_{static}  = V \cdot N \cdot K_{design} \cdot I_{leak}
+ \textit P_{static}  = V \cdot N \cdot K_{design} \cdot I_{leak}
 \end{equation}
 where V is the supply voltage, N is the number of transistors, $K_{design}$ is a
 design dependent parameter and $I_{leak}$ is a technology-dependent
 parameter. Energy consumed by an individual processor $E_{ind}$ is the summation
 of the dynamic and the static power multiply by the execution time for example
-see~\cite{36,15} .
+see~\cite{36,15}.
 \begin{equation}
   \label{eq:eind}
-  E_{ind} = ( P_{dyn} + P_{static} ) \cdot T
+  \textit E_{ind} = ( P_{dyn} + P_{static} ) \cdot T
 \end{equation}
 The dynamic voltage and frequency scaling (DVFS) is a process that allowed in
 modern processors to reduce the dynamic power by scaling down the voltage and
 frequency. Its main objective is to reduce the overall energy
 consumption~\cite{37}. The operational frequency \emph f depends linearly on the
-supply voltage $V$, i.e., $V = \beta . f$ with some constant $\beta$. This
+supply voltage $V$, i.e., $V = \beta \cdot f$ with some constant $\beta$. This
 equation is used to study the change of the dynamic voltage with respect to
 various frequency values in~\cite{3}. The reduction process of the frequency are
 expressed by scaling factor \emph S. The scale \emph S is the ratio between the
 maximum and the new frequency as in EQ~(\ref{eq:s}).
 \begin{equation}
   \label{eq:s}
-  S = \frac{F_{max}}{F_{new}}
+ S = \frac{F_{max}}{F_{new}}
 \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
+The value of the scale $S$ is greater than 1 when changing the frequency to
+any new frequency value (\emph {P-state}) in governor.
+\AG{Explain what's a 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
@@ -251,11 +274,12 @@ derivation for this equation (to be minimized) and set it to zero to produce the
 scaling factor as in EQ~(\ref{eq:sopt}).
 \begin{equation}
   \label{eq:sopt}
-  S_{opt} = \sqrt[3]{\frac{2}{n} \cdot \frac{P_{dyn}}{P_{static}} \cdot
+ \textit  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{equation}
 
 \section{Performance Evaluation of MPI Programs}
+\label{sec.mpip}
 
 The performance (execution time) of the parallel MPI applications are depends on
 the time of the slowest task as in figure~(\ref{fig:homo}). Normally the
@@ -283,7 +307,7 @@ any MPI program as a function of the new scaling factor as in the
 EQ~(\ref{eq:tnew}).
 \begin{equation}
   \label{eq:tnew}
-  T_{new} = T_{\textit{Max Comp Old}} \cdot S + T_{\textit{Max Comm Old}}
+ \textit  T_{new} = T_{\textit{Max Comp Old}} \cdot S + T_{\textit{Max Comm Old}}
 \end{equation}
 The above equation shows that the scaling factor \emph S has linear relation
 with the computation time without affecting the communication time. The
@@ -295,6 +319,7 @@ method as we will show in the coming sections. In the next section we make an
 investigation study for the EQ~(\ref{eq:tnew}).
 
 \section{Performance Prediction Verification}
+\label{sec.verif}
 
 In this section we evaluate the precision of our performance prediction methods
 on the NAS benchmark. We use the EQ~(\ref{eq:tnew}) that predicts the execution
@@ -325,9 +350,11 @@ example, we are present the execution times of the NAS benchmarks as in the
 figure~(\ref{fig:pred}).
 
 \section{Performance to Energy Competition}
+\label{sec.compet}
+
 This section demonstrates our approach for choosing the optimal scaling
 factor. This factor gives maximum energy reduction taking into account the
-execution time for both computation and communication times . The relation
+execution time for both computation and communication times. The relation
 between the energy and the performance are nonlinear and complex, because the
 relation of the energy with scaling factor is nonlinear and with the performance
 it is linear see~\cite{17}. The relation between the energy and the performance
@@ -337,8 +364,8 @@ between the consumed energy with scaled frequency and the consumed energy
 without scaled frequency :
 \begin{multline}
   \label{eq:enorm}
-  E_\textit{Norm} = \frac{E_{Reduced}}{E_{Original}}\\
-  {} = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
+ \textit E_{Norm} = \frac{\textit E_{Reduced}}{\textit E_{Original}} \\
+        {} = \frac{ P_{dyn} \cdot S_i^{-2} \cdot
                \left( T_1 + \sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
                P_{static} \cdot T_1 \cdot S_i \cdot N  }{
               P_{dyn} \cdot \left(T_1+\sum_{i=2}^{N}\frac{T_i^3}{T_1^2}\right) +
@@ -354,9 +381,9 @@ without scaled frequency :
 By the same way we can normalize the performance as follows :
 \begin{equation}
   \label{eq:pnorm}
-  P_{Norm} = \frac{T_{New}}{T_{Old}}
+\textit  P_{Norm} = \frac{\textit T_{New}}{\textit T_{Old}}
           = \frac{T_{\textit{Max Comp Old}} \cdot S +
-              T_{\textit{Max Comm Old}}}{T_{Old}}
+           T_{\textit{Max Comm Old}}}{\textit T_{Old}}
 \end{equation}
 The second problem is the optimization operation for both energy and performance
 is not in the same direction. In other words, the normalized energy and the
@@ -375,17 +402,17 @@ have the same direction. Therefore, we inverse the equation of normalize
 performance as follows :
 \begin{equation}
   \label{eq:pnorm_en}
-  P^{-1}_{Norm} = \frac{T_{Old}}{T_{New}}
-               = \frac{T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
+\textit  P^{-1}_{Norm} = \frac{\textit T_{Old}}{\textit T_{New}}
+               = \frac{\textit T_{Old}}{T_{\textit{Max Comp Old}} \cdot S +
                  T_{\textit{Max Comm Old}}}
 \end{equation}
 \begin{figure*}
   \centering
   \subfloat[Converted Relation.]{%
-    \includegraphics[width=.4\textwidth]{file.eps}\label{fig:r1}}%
+    \includegraphics[width=.33\textwidth]{file.eps}\label{fig:r1}}%
   \qquad%
   \subfloat[Real Relation.]{%
-    \includegraphics[width=.4\textwidth]{file3.eps}\label{fig:r2}}
+    \includegraphics[width=.33\textwidth]{file3.eps}\label{fig:r2}}
   \label{fig:rel}
   \caption{The Energy and Performance Relation}
 \end{figure*}
@@ -397,8 +424,8 @@ in the same time, see figure~(\ref{fig:r1}). Then our objective function has the
 following form:
 \begin{equation}
   \label{eq:max}
-  \textit{MaxDist} = \max (\overbrace{P^{-1}_{Norm}}^{\text{Maximize}} -
-                           \overbrace{E_{Norm}}^{\text{Minimize}} )
+  \textit{MaxDist} = \max (\overbrace{\textit P^{-1}_{Norm}}^{\text{Maximize}} -
+                           \overbrace{\textit E_{Norm}}^{\text{Minimize}} )
 \end{equation}
 Then we can select the optimal scaling factor that satisfy the
 EQ~(\ref{eq:max}).  Our objective function can works with any energy model or
@@ -409,6 +436,7 @@ objective of this paper and we choose Rauber's model as an example with two
 reasons that mentioned before.
 
 \section{Optimal Scaling Factor for Performance and Energy}
+\label{sec.optim}
 
 In the previous section we described the objective function that satisfy our
 goal in discovering optimal scaling factor for both performance and energy at
@@ -462,8 +490,7 @@ in the MPI program.
   \State -Computations Section.
    \State -Communications Section.
    \If {$(J==1)$} 
-     \State -Gather all times of computation and\par
-        \State      communication from each node.
+     \State -Gather all times of computation and communication from\par each node.
      \State -Call EPSA with these times.
      \State -Calculate the new frequency from optimal scale.
      \State -Set the new frequency to the system.
@@ -486,6 +513,7 @@ have imbalanced workloads. Then EQ~(\ref{eq:fi}) works in adaptive way to change
 the frequency according to the nodes workloads.
 
 \section{Experimental Results}
+\label{sec.expe}
 
 The proposed EPSA algorithm was applied to seven MPI programs of the NAS
 benchmarks (EP, CG, MG, FT, BT, LU and SP). We work on three classes (A, B and
@@ -500,7 +528,7 @@ detailed characteristics of our platform file are shown in the
 table~(\ref{table:platform}). Each node in the cluster has 18 frequency values
 from 2.5 GHz to 800 MHz with 100 MHz difference between each two successive
 frequencies.
-\begin{table}[ht]
+\begin{table}[htb]
   \caption{Platform File Parameters}
   % title of Table
   \centering
@@ -508,7 +536,7 @@ frequencies.
     \hline
     Max & Min & Backbone & Backbone&Link &Link& Sharing  \\
     Freq. & Freq. & Bandwidth & Latency & Bandwidth& Latency&Policy  \\ \hline
-    2.5 &800 & 2.25 GBps &$5\times 10^{-7} s$& 1 GBps & $5\times 10^{-5}$ s&Full  \\
+    2.5 &800 & 2.25 GBps &$5\times 10^{-7} s$& 1 GBps & $5\times 10^{-5} s$ &Full  \\
     GHz& MHz&  & & &  &Duplex  \\\hline
   \end{tabular}
   \label{table:platform}
@@ -532,7 +560,7 @@ programs. In table~(\ref{table:factors results}), we record all optimal scaling
 factors results for each program on class C. These factors give the maximum
 energy saving percent and the minimum performance degradation percent in the
 same time over all available scales.
-\begin{figure*}
+\begin{figure*}[t]
   \centering
   \includegraphics[width=.33\textwidth]{ep.eps}\hfill%
   \includegraphics[width=.33\textwidth]{cg.eps}\hfill%
@@ -543,7 +571,7 @@ same time over all available scales.
   \caption{Optimal scaling factors for The NAS MPI Programs}
   \label{fig:nas}
 \end{figure*}
-\begin{table}
+\begin{table}[htb]
   \caption{Optimal Scaling Factors Results}
   % title of Table
   \centering
@@ -561,7 +589,7 @@ same time over all available scales.
     BT & 1.31 &29.60&21.28 &8.32\\ \hline
     SP & 1.38 &33.48&21.36 &12.12\\ \hline
     FT & 1.47 &34.72&19.00 &15.72\\ \hline
-  \end{tabular}
+  \end{tabular}	
   \label{table:factors results}
   % is used to refer this table in the text
 \end{table}
@@ -575,6 +603,7 @@ cases. In EP there are no communications inside the iterations. This make our
 EPSA to selects smaller scaling factor values (inducing smaller energy savings).
 
 \section{Comparing Results}
+\label{sec.compare}
 
 In this section, we compare our EPSA algorithm results with Rauber's
 methods~\cite{3}. He had two scenarios, the first is to reduce energy to optimal
@@ -586,7 +615,7 @@ 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.
-\begin{table}[ht]
+\begin{table*}[p]
   \caption{Comparing Results for  The NAS Class A}
   % title of Table
   \centering
@@ -626,8 +655,8 @@ benchmarks programs for classes A,B and C.
   \end{tabular}
   \label{table:compare Class A}
   % is used to refer this table in the text
-\end{table}
-\begin{table}[ht]
+\end{table*}
+\begin{table*}[p]
   \caption{Comparing Results for The NAS Class B}
   % title of Table
   \centering
@@ -667,9 +696,9 @@ benchmarks programs for classes A,B and C.
   \end{tabular}
   \label{table:compare Class B}
   % is used to refer this table in the text
-\end{table}
+\end{table*}
 
-\begin{table}[ht]
+\begin{table*}[p]
   \caption{Comparing Results for The NAS Class C}
   % title of Table
   \centering
@@ -709,7 +738,7 @@ benchmarks programs for classes A,B and C.
   \end{tabular}
 \label{table:compare Class C}
 % is used to refer this table in the text
-\end{table}
+\end{table*}
 As shown in these tables our scaling factor is not optimal for energy saving
 such as Rauber's scaling factor EQ~(\ref{eq:sopt}), but it is optimal for both
 the energy and the performance simultaneously. Our EPSA optimal scaling factors
@@ -731,25 +760,32 @@ concatenating with less performance degradation and this the objective of this
 paper. While the negative trade offs refers to improving energy saving (or may
 be the performance) while degrading the performance (or may be the energy) more
 than the first.
-\begin{figure*}
+\begin{figure}[t]
   \centering
-  \includegraphics[width=.33\textwidth]{compare_class_A.pdf}\hfill%
-  \includegraphics[width=.33\textwidth]{compare_class_B.pdf}\hfill%
+  \includegraphics[width=.33\textwidth]{compare_class_A.pdf}
+  \includegraphics[width=.33\textwidth]{compare_class_B.pdf}
   \includegraphics[width=.33\textwidth]{compare_class_c.pdf}
   \caption{Comparing Our EPSA with Rauber's Methods}
   \label{fig:compare}
-\end{figure*}
+\end{figure}
 
 \section{Conclusion}
-\label{sec.conc}
+\label{sec.concl}
 
 \AG{the conclusion needs to be written\dots{} one day}
 
 \section*{Acknowledgment}
 
+\AG{Right?}
 Computations have been performed on the supercomputer facilities of the
 MÃ©socentre de calcul de Franche-ComtÃ©.
 
+% trigger a \newpage just before the given reference
+% number - used to balance the columns on the last page
+% adjust value as needed - may need to be readjusted if
+% the document is modified later
+%\IEEEtriggeratref{15}
+
 \bibliographystyle{IEEEtran}
 \bibliography{IEEEabrv,my_reference}
 \end{document}
@@ -758,8 +794,8 @@ MÃ©socentre de calcul de Franche-ComtÃ©.
 %%% mode: latex
 %%% TeX-master: t
 %%% fill-column: 80
-%%%ispell-local-dictionary: "american"
+%%% ispell-local-dictionary: "american"
 %%% End:
 
 %  LocalWords:  Badri Charr FIXME Tianhe DVFS HPC NAS NPB SMPI Rauber's Rauber
-%  LocalWords:  CMOS EQ EPSA
+%  LocalWords:  CMOS EQ EPSA Franche ComtÃ© Tflop
