From a88840386a8fd302d0460659690d13732a9f3a38 Mon Sep 17 00:00:00 2001
From: jccharr <jccharr@charr.local>
Date: Tue, 28 Oct 2014 15:40:57 +0100
Subject: [PATCH] section IV corrected

---
 Heter_paper.tex | 28 ++++++++++++++++------------
 1 file changed, 16 insertions(+), 12 deletions(-)

diff --git a/Heter_paper.tex b/Heter_paper.tex
index c6f3021..8c329a8 100644
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -267,20 +267,25 @@ In the same way, we normalize the energy by computing the ratio between the cons
 \end{multline} 
 Where $T_{New}$ and $T_{Old}$ are computed as in EQ(\ref{eq:pnorm}).
 
-  The normalized energy and execution time curves are not in the same direction.   While the main
-goal is to optimize the energy and execution time at the same time.  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 set 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.  Many researchers used
+reduction with minimum execution time reduction.  
+
+Many researchers used
 different strategies to solve this nonlinear problem for example
-see~\cite{19,42}, their methods add big overheads to the algorithm to select the
-suitable frequency.  In this paper we are present a method to find the optimal
-set of frequency scaling factors to optimize both energy and execution time
-simultaneously without adding a big overhead.  Our solution for this problem is
+in~\cite{19,42}, their methods add big overheads to the algorithm to select the
+suitable frequency.  In this paper we  present a method to find the optimal
+set of frequency scaling factors to simultaneously optimize both energy and execution time
+ without adding a big overhead. \textbf{put the last two phrases in the related work section}
+ 
+  
+    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,
-the normalized performance, as follows:
+direction.  Therefore, we inverse the equation of the normalized execution time which gives 
+the normalized performance equation, as follows:
 \begin{multline}
   \label{eq:pnorm_inv}
   P_\textit{Norm} = \frac{T_\textit{Old}}{T_\textit{New}}\\
@@ -315,9 +320,8 @@ function has the following form:
 \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 energy values stored in a data file.
-Moreover, this function works in optimal way when the energy curve has a convex
-form over the available frequency scaling factors as shown in~\cite{15,3,19}.
+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 the energy curve has a convex form as shown in~\cite{15,3,19}.
 
 \section{The heterogeneous scaling algorithm }
 \label{sec.optim}
-- 
2.39.5