reduced the we

diff --git a/Heter_paper.tex b/Heter_paper.tex
index ec89460ab3efd41c376e64e28ca4ea17a8365b86..90793bf0c200e42d0e8a0d6859cb926c3cf68c55 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -132,7 +132,7 @@ Section~\ref{sec.optim} details the proposed frequency selecting algorithm then
 Section~\ref{sec.expe} presents the results of applying the algorithm on  the NAS parallel benchmarks and executing them 
 on a heterogeneous platform. It also shows the results of running three 
 different power scenarios and comparing them. 
 Section~\ref{sec.expe} presents the results of applying the algorithm on  the NAS parallel benchmarks and executing them 
 on a heterogeneous platform. It also shows the results of running three 
 different power scenarios and comparing them. 

-Finally, we conclude in Section~\ref{sec.concl} with a summary and some future works.
+Finally, in Section~\ref{sec.concl} the paper is ended with a summary and some future works.

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


@@ -196,7 +196,7 @@ In contrast to the above described papers, this paper presents the following con
 
 In this paper, we are interested in reducing the energy consumption of message
 passing distributed iterative synchronous applications running over
 
 In this paper, we are interested in reducing the energy consumption of message
 passing distributed iterative synchronous applications running over

-heterogeneous platforms. We define a heterogeneous platform as a collection of
+heterogeneous platforms. A heterogeneous platform is defined as a collection of

 heterogeneous computing nodes interconnected via a high speed homogeneous
 network. Therefore, each node has different characteristics such as computing
 power (FLOPS), energy consumption, CPU's frequency range, \dots{} but they all
 heterogeneous computing nodes interconnected via a high speed homogeneous
 network. Therefore, each node has different characteristics such as computing
 power (FLOPS), energy consumption, CPU's frequency range, \dots{} but they all


@@ -282,7 +282,7 @@ to compute the best scaling factors vector.  The algorithm complexity is $O(F\cd
 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 sections (\ref{sec.res}) and (\ref{sec.compare}).
 slowest node, it means  only the  communication time without any slack time. 
 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 sections (\ref{sec.res}) and (\ref{sec.compare}).
 slowest node, it means  only the  communication time without any slack time. 

-Therefore, we can consider the execution time of the iterative application is 
+Therefore, the execution time of the iterative application is 

 equal to the execution time of one iteration as in EQ(\ref{eq:perf}) multiplied 
 by the number of iterations of that application.
 
 equal to the execution time of one iteration as in EQ(\ref{eq:perf}) multiplied 
 by the number of iterations of that application.
 


@@ -330,8 +330,8 @@ voltage with respect to various frequency values in~\cite{Rauber_Analytical.Mode
 process of the frequency can be expressed by the scaling factor $S$ which is the
 ratio between the maximum and the new frequency as in EQ(\ref{eq:s}).
 The CPU governors are power schemes supplied by the operating
 process of the frequency can be expressed by the scaling factor $S$ which is the
 ratio between the maximum and the new frequency as in EQ(\ref{eq:s}).
 The CPU governors are power schemes supplied by the operating

-system's kernel to lower a core's frequency. we can calculate the new frequency 
-$F_{new}$ from EQ(\ref{eq:s}) as follow:
+system's kernel to lower a core's frequency. The new frequency 
+$F_{new}$ from EQ(\ref{eq:s}) can be calculated as follows:

 \begin{equation}
   \label{eq:fnew}
    F_\textit{new} = S^{-1} \cdot F_\textit{max}
 \begin{equation}
   \label{eq:fnew}
    F_\textit{new} = S^{-1} \cdot F_\textit{max}


@@ -357,7 +357,7 @@ and is given by the following equation:
 \end{equation}
 The static power is related to the power leakage of the CPU and is consumed during computation 
 and even when idle. As in~\cite{Rauber_Analytical.Modeling.for.Energy,Zhuo_Energy.efficient.Dynamic.Task.Scheduling}, 
 \end{equation}
 The static power is related to the power leakage of the CPU and is consumed during computation 
 and even when idle. As in~\cite{Rauber_Analytical.Modeling.for.Energy,Zhuo_Energy.efficient.Dynamic.Task.Scheduling}, 

-we assume that the static power of a processor is constant 
+ the static power of a processor is considered as constant 

 during idle and computation periods, and for all its available frequencies. 
 The static energy is the static power multiplied by the execution time of the program. 
 According to the execution time model in EQ(\ref{eq:perf}), the execution time of the program 
 during idle and computation periods, and for all its available frequencies. 
 The static energy is the static power multiplied by the execution time of the program. 
 According to the execution time model in EQ(\ref{eq:perf}), the execution time of the program 


@@ -392,8 +392,8 @@ for each  processor.  It is computed as follows:
 Reducing the frequencies of the processors according to the vector of
 scaling factors $(S_1, S_2,\dots, S_N)$ may degrade the performance of the
 application and thus, increase the static energy because the execution time is
 Reducing the frequencies of the processors according to the vector of
 scaling factors $(S_1, S_2,\dots, S_N)$ may degrade the performance of the
 application and thus, increase the static energy because the execution time is

-increased~\cite{Kim_Leakage.Current.Moore.Law}. We can measure the overall energy consumption for the iterative 
-application by measuring  the energy consumption for one iteration as in EQ(\ref{eq:energy}) 
+increased~\cite{Kim_Leakage.Current.Moore.Law}. The overall energy consumption for the iterative 
+application can be measured by measuring  the energy consumption for one iteration as in EQ(\ref{eq:energy}) 

 multiplied by the number of iterations of that application.
 
 
 multiplied by the number of iterations of that application.
 
 


@@ -422,8 +422,8 @@ The relation between the energy consumption and the execution time for an applic
 complex and nonlinear, Thus, unlike the relation between the execution time 
 and the scaling factor, the relation of the energy with the frequency scaling
 factors is nonlinear, for more details refer to~\cite{Freeh_Exploring.the.Energy.Time.Tradeoff}.  
 complex and nonlinear, Thus, unlike the relation between the execution time 
 and the scaling factor, the relation of the energy with the frequency scaling
 factors is nonlinear, for more details refer to~\cite{Freeh_Exploring.the.Energy.Time.Tradeoff}.  

-Moreover, they are not measured using the same metric.  To solve this problem, we normalize the
-execution time by computing the ratio between the new execution time (after 
+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:
 \begin{multline}
 scaling down the frequencies of some processors) and the initial one (with maximum 
 frequency for all nodes,) as follows:
 \begin{multline}


@@ -434,7 +434,7 @@ frequency for all nodes,) as follows:
 \end{multline}
 
 
 \end{multline}
 
 

-In the same way, we normalize the energy by computing the ratio between the consumed energy 
+In the same way, the energy is normalized by computing the ratio between the consumed energy 

 while scaling down the frequency and the consumed energy with maximum frequency for all nodes:
 \begin{multline}
   \label{eq:enorm}
 while scaling down the frequency and the consumed energy with maximum frequency for all nodes:
 \begin{multline}
   \label{eq:enorm}


@@ -455,9 +455,9 @@ reduction with minimum execution time reduction.
 
  
   
 
  
   

-Our solution for this problem is to make the optimization process for energy and 
-execution time follow the same direction.  Therefore, we inverse the equation of the 
-normalized execution time which gives the normalized performance equation, as follows:
+This problem can be solved by making the optimization process for energy and 
+execution time follow the same direction.  Therefore, the equation of the 
+normalized execution time is inverted which gives the normalized performance equation, as follows:

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


@@ -477,7 +477,7 @@ normalized execution time which gives the normalized performance equation, as fo
   \caption{The energy and performance relation}
 \end{figure}
 
   \caption{The energy and performance relation}
 \end{figure}
 

-Then, we can model our objective function as finding the maximum distance
+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:pnorm_inv}) over all available sets of scaling factors.  This
 represents the minimum energy consumption with minimum execution time (maximum 
 between the energy curve EQ~(\ref{eq:enorm}) and the  performance
 curve EQ~(\ref{eq:pnorm_inv}) over all available sets of scaling factors.  This
 represents the minimum energy consumption with minimum execution time (maximum 


@@ -491,8 +491,8 @@ function has the following form:
        \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. 
        \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 we can select the optimal set of scaling factors that satisfies EQ~(\ref{eq:max}).  
-Our objective function can work with any energy model or any power values for each node 
+Then, the optimal set of scaling factors that satisfies EQ~(\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}.
 
 (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}.
 


@@ -500,7 +500,7 @@ 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 we  propose algorithm~(\ref{HSA}) which 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.  


@@ -1055,8 +1055,7 @@ results in less energy saving but less performance degradation.
 
 \section{Conclusion}
 \label{sec.concl} 
 
 \section{Conclusion}
 \label{sec.concl} 

-In this paper, we have presented a new online selecting frequency scaling factors algorithm
-that selects the best possible vector of frequency scaling factors for a heterogeneous platform. 
+In this paper, a new online frequency selecting algorithm have been presented. It selects the best possible vector of frequency scaling factors for a heterogeneous platform. 

 This vector gives the maximum distance (optimal tradeoff) between the predicted energy and 
 the predicted performance curves. In addition, we developed a new energy model for measuring  
 and predicting the energy of distributed iterative applications running over heterogeneous 
 This vector gives the maximum distance (optimal tradeoff) between the predicted energy and 
 the predicted performance curves. In addition, we developed a new energy model for measuring  
 and predicting the energy of distributed iterative applications running over heterogeneous