some corrections

diff --git a/Heter_paper.tex b/Heter_paper.tex
index d2180d904ec37af141ef961e3e2e8289a23dc89d..f34524c8eea7c8969751c9fffa2de636c3550266 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -53,7 +53,7 @@
 \newcommand{\Told}{\Xsub{T}{Old}} 
 \begin{document} 
 
 \newcommand{\Told}{\Xsub{T}{Old}} 
 \begin{document} 
 

-\title{Energy Consumption Reduction in a Heterogeneous Architecture Using DVFS}
+\title{Energy Consumption Reduction for Message Passing Iterative  Applications in Heterogeneous Architecture Using DVFS}

  
 \author{% 
   \IEEEauthorblockN{%
  
 \author{% 
   \IEEEauthorblockN{%


@@ -84,10 +84,10 @@ Therefore, the frequency that gives the best  tradeoff between the energy consum
 application must be selected. 
 
 In this paper, a new online frequencies selecting algorithm for heterogeneous platforms is presented. 
 application must be selected. 
 
 In this paper, a new online frequencies selecting algorithm for heterogeneous platforms is presented. 

-It selects the frequency that give the best tradeoff between energy saving and performance degradation, 
+It selects the frequency that try to give the best tradeoff between energy saving and performance degradation, 

 for each node computing the message passing iterative application. The algorithm has a small overhead and 
 works without training or profiling. It uses a new energy model for message passing iterative applications 
 for each node computing the message passing iterative application. The algorithm has a small overhead and 
 works without training or profiling. It uses a new energy model for message passing iterative applications 

-running on a heterogeneous platform. The proposed algorithm evaluated  on the Simgrid simulator while 
+running on a heterogeneous platform. The proposed algorithm is evaluated  on the Simgrid simulator while 

 running the NAS parallel benchmarks. The experiments demonstrated that it reduces the energy consumption 
 up to 35\% while limiting the performance degradation as much as possible.
 \end{abstract}
 running the NAS parallel benchmarks. The experiments demonstrated that it reduces the energy consumption 
 up to 35\% while limiting the performance degradation as much as possible.
 \end{abstract}


@@ -107,7 +107,7 @@ Tianhe-2 platform is approximately more than \$10 millions each year.
 The computing platforms must be more energy efficient and offer the highest number of FLOPS per watt possible, 
 such as the L-CSC from the GSI Helmholtz Center which  
 became the top of the Green500 list in November 2014 \cite{Green500_List}. 
 The computing platforms must be more energy efficient and offer the highest number of FLOPS per watt possible, 
 such as the L-CSC from the GSI Helmholtz Center which  
 became the top of the Green500 list in November 2014 \cite{Green500_List}. 

-This heterogeneous platform executes more than 5  GFLOPS per watt while consuming 57.15 kilowatts.
+This heterogeneous platform executes more than 5  GFLOPS per watt while consumed 57.15 kilowatts.

 
 Besides hardware improvements, there are many software techniques to lower the energy consumption of these platforms, 
 such as scheduling, DVFS, ... DVFS is a widely  used process to reduce the energy consumption of a processor by lowering 
 
 Besides hardware improvements, there are many software techniques to lower the energy consumption of these platforms, 
 such as scheduling, DVFS, ... DVFS is a widely  used process to reduce the energy consumption of a processor by lowering 


@@ -403,7 +403,7 @@ factors is nonlinear, for more details refer to~\cite{Freeh_Exploring.the.Energy
 Moreover, they are not measured using the same metric.  To solve this problem,  the
 execution time is normalized by computing the ratio between the new execution time (after 
 scaling down the frequencies of some processors) and the initial one (with maximum 
 Moreover, they are not measured using the same metric.  To solve this problem,  the
 execution time is normalized by computing the ratio between the new execution time (after 
 scaling down the frequencies of some processors) and the initial one (with maximum 

-frequency for all nodes,) as follows:
+frequency for all nodes) as follows:

 \begin{multline}
   \label{eq:pnorm}
   P_\textit{Norm} = \frac{T_\textit{New}}{T_\textit{Old}}\\
 \begin{multline}
   \label{eq:pnorm}
   P_\textit{Norm} = \frac{T_\textit{New}}{T_\textit{Old}}\\


@@ -427,7 +427,7 @@ Where $E_\textit{Reduced}$ and $E_\textit{Original}$ are computed using (\ref{eq
 While the main 
 goal is to optimize the energy and execution time at the same time, the normalized 
 energy and execution time curves are not in the same direction. According 
 While the main 
 goal is to optimize the energy and execution time at the same time, the normalized 
 energy and execution time curves are not in the same direction. According 

-to the equations~(\ref{eq:enorm}) and~(\ref{eq:pnorm}), the vector  of frequency
+to the equations~(\ref{eq:pnorm}) and (\ref{eq:enorm}), the vector  of frequency

 scaling factors $S_1,S_2,\dots,S_N$ reduce both the energy and the execution
 time simultaneously.  But the main objective is to produce maximum energy
 reduction with minimum execution time reduction.  
 scaling factors $S_1,S_2,\dots,S_N$ reduce both the energy and the execution
 time simultaneously.  But the main objective is to produce maximum energy
 reduction with minimum execution time reduction.  


@@ -456,8 +456,8 @@ normalized execution time is inverted which gives the normalized performance equ
 \end{figure}
 
 Then, the objective function can be modeled   as finding the maximum distance
 \end{figure}
 
 Then, the objective function can be modeled   as finding the maximum distance

-between the energy curve EQ~(\ref{eq:enorm}) and the  performance
-curve EQ~(\ref{eq:pnor@+eYd162m_inv}) over all available sets of scaling factors.  This
+between the energy curve (\ref{eq:enorm}) and the  performance
+curve (\ref{eq:pnorm_inv}) over all available sets of scaling factors.  This

 represents the minimum energy consumption with minimum execution time (maximum 
 performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then the objective
 function has the following form:
 represents the minimum energy consumption with minimum execution time (maximum 
 performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then the objective
 function has the following form:


@@ -468,8 +468,8 @@ function has the following form:
       (\overbrace{P_\textit{Norm}(S_{ij})}^{\text{Maximize}} -
        \overbrace{E_\textit{Norm}(S_{ij})}^{\text{Minimize}} )
 \end{equation}
       (\overbrace{P_\textit{Norm}(S_{ij})}^{\text{Maximize}} -
        \overbrace{E_\textit{Norm}(S_{ij})}^{\text{Minimize}} )
 \end{equation}

-where $N$ is the number of nodes and $F$ is the  number of available frequencies for each nodes. 
-Then, the optimal set of scaling factors that satisfies EQ~(\ref{eq:max}) can be selected.  
+where $N$ is the number of nodes and $F$ is the  number of available frequencies for each node. 
+Then, the optimal set of scaling factors that satisfies (\ref{eq:max}) can be selected.  

 The objective function can work with any energy model or any power values for each node 
 (static and dynamic powers). However, the most energy reduction gain can be achieved when 
 the energy curve has a convex form as shown in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modeling.for.Energy,Hao_Learning.based.DVFS}.
 The objective function can work with any energy model or any power values for each node 
 (static and dynamic powers). However, the most energy reduction gain can be achieved when 
 the energy curve has a convex form as shown in~\cite{Zhuo_Energy.efficient.Dynamic.Task.Scheduling,Rauber_Analytical.Modeling.for.Energy,Hao_Learning.based.DVFS}.


@@ -478,7 +478,7 @@ the energy curve has a convex form as shown in~\cite{Zhuo_Energy.efficient.Dynam
 \label{sec.optim}
 
 \subsection{The algorithm details}
 \label{sec.optim}
 
 \subsection{The algorithm details}

-In this section algorithm~(\ref{HSA}) is presented. It selects the frequency scaling factors 
+In this section algorithm \ref{HSA} is presented. It selects the frequency scaling factors 

 vector that gives the best trade-off between minimizing the energy consumption  and maximizing 
 the performance of a message passing synchronous iterative application executed on a heterogeneous 
 platform. It works online during the execution time of the iterative message passing program.  
 vector that gives the best trade-off between minimizing the energy consumption  and maximizing 
 the performance of a message passing synchronous iterative application executed on a heterogeneous 
 platform. It works online during the execution time of the iterative message passing program.  


@@ -569,12 +569,11 @@ which results in bigger energy savings.
     \State Round the computed initial frequencies $F_i$ to the closest one available in each node.
     \If{(not the first frequency)}
           \State $F_i \gets F_i+Fdiff_i,~i=1,\dots,N.$
     \State Round the computed initial frequencies $F_i$ to the closest one available in each node.
     \If{(not the first frequency)}
           \State $F_i \gets F_i+Fdiff_i,~i=1,\dots,N.$

-          \State where $i=1,\dots,N$ means for loop.

     \EndIf 
     \State $T_\textit{Old} \gets max_{~i=1,\dots,N } (Tcp_i+Tcm_i)$
     \State $E_\textit{Original} \gets \sum_{i=1}^{N}{( Pd_i \cdot  Tcp_i)} +\sum_{i=1}^{N} {(Ps_i \cdot T_{Old})}$
     \EndIf 
     \State $T_\textit{Old} \gets max_{~i=1,\dots,N } (Tcp_i+Tcm_i)$
     \State $E_\textit{Original} \gets \sum_{i=1}^{N}{( Pd_i \cdot  Tcp_i)} +\sum_{i=1}^{N} {(Ps_i \cdot T_{Old})}$

-    \State  $Sopt_{i} \gets \frac{Fmax_i}{F_i},~i=1,\dots,N. $
-    \State Computing the initial distance  $Dist \gets\Pnorm(Sopt_i) - \Enorm(Sopt_i) $
+    \State  $Sopt_{i} \gets 1,~i=1,\dots,N. $
+    \State $Dist \gets 0 $

     \While {(all nodes not reach their  minimum  frequency)}
         \If{(not the last freq. \textbf{and} not the slowest node)}
         \State $F_i \gets F_i - Fdiff_i,~i=1,\dots,N.$
     \While {(all nodes not reach their  minimum  frequency)}
         \If{(not the last freq. \textbf{and} not the slowest node)}
         \State $F_i \gets F_i - Fdiff_i,~i=1,\dots,N.$


@@ -616,7 +615,7 @@ which results in bigger energy savings.
   \label{dvfs}
 \end{algorithm}
 
   \label{dvfs}
 \end{algorithm}
 

-\subsection{The verifications of the proposed algorithm}
+\subsection{The evaluation of the proposed algorithm}

 \label{sec.verif.algo}
 The precision of the proposed algorithm mainly depends on the execution time prediction model defined in 
 (\ref{eq:perf}) and the energy model computed by (\ref{eq:energy}). 
 \label{sec.verif.algo}
 The precision of the proposed algorithm mainly depends on the execution time prediction model defined in 
 (\ref{eq:perf}) and the energy model computed by (\ref{eq:energy}). 


@@ -635,7 +634,7 @@ that tests all the possible solutions. The brute force algorithm was applied to
 different number of nodes. The solutions returned by the brute force algorithm and the proposed algorithm were identical 
 and the proposed algorithm was on average 10 times faster than the brute force algorithm. It has a small execution time: 
 for a heterogeneous cluster composed of four different types of nodes having the characteristics presented in 
 different number of nodes. The solutions returned by the brute force algorithm and the proposed algorithm were identical 
 and the proposed algorithm was on average 10 times faster than the brute force algorithm. It has a small execution time: 
 for a heterogeneous cluster composed of four different types of nodes having the characteristics presented in 

-table~(\ref{table:platform}), it takes on average \np[ms]{0.04}  for 4 nodes and \np[ms]{0.15} on average for 144 nodes 
+table~\ref{table:platform}, it takes on average \np[ms]{0.04}  for 4 nodes and \np[ms]{0.15} on average for 144 nodes 

 to compute the best scaling factors vector.  The algorithm complexity is $O(F\cdot (N \cdot4) )$, where $F$ is the number 
 of iterations and $N$ is the number of computing nodes. The algorithm needs  from 12 to 20 iterations to select the best 
 vector of frequency scaling factors that gives the results of the next sections.
 to compute the best scaling factors vector.  The algorithm complexity is $O(F\cdot (N \cdot4) )$, where $F$ is the number 
 of iterations and $N$ is the number of computing nodes. The algorithm needs  from 12 to 20 iterations to select the best 
 vector of frequency scaling factors that gives the results of the next sections.

diff --git a/fig/commtasks.pdf b/fig/commtasks.pdf
index 5c891e9f1ae6abaf3152d4bc1086576fe4a413cd..0e39a6d6e966be2bb2ae57da77b4096c95b5a4c9 100644 (file)
Binary files a/fig/commtasks.pdf and b/fig/commtasks.pdf differ