add fig.

diff --git a/Heter_paper.tex b/Heter_paper.tex
index e9f6b67dc67f73de52ea6f73b85ccacfe72da6ba..66dab369171cb1d48e8caf2e3b1c2f5b29e17610 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -340,10 +340,13 @@ maximum frequency of node $i$  and the computation scaling factor $Scp_i$ as fol
  F_{i} = \frac{Fmax_i}{Scp_i},~{i=1,2,\cdots,N}
 \end{equation}
 If the computed initial frequency for a node is not available in the gears of that node, the computed initial frequency is replaced by the nearest available frequency.
  F_{i} = \frac{Fmax_i}{Scp_i},~{i=1,2,\cdots,N}
 \end{equation}
 If the computed initial frequency for a node is not available in the gears of that node, the computed initial frequency is replaced by the nearest available frequency.

-In  figure (\ref{fig:st_freq}), the nodes are  sorted by their computing powers in ascending order and the frequencies of the faster nodes are scaled down according to the computed initial frequency scaling factors. The resulting new frequencies are colored in blue in  figure (\ref{fig:st_freq}). This set of frequencies can be considered as a higher bound for the search space of the optimal set of frequencies because selecting frequency scaling factors higher than the higher bound will not improve the performance of the application and it will increase its overall energy consumption. Therefore the frequency selecting factors algorithm starts its search method from these initial frequencies and takes a downward search direction. The algorithm iterates on all left frequencies, from the higher bound until all nodes reach their minimum frequencies, to compute their overall energy consumption and performance, and select the optimal frequency scaling factors vector. At each iteration the algorithm determines the slowest node according to EQ(\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of  all other nodes by one gear. The new overall energy consumption and execution time are computed according to the new scaling factors. The optimal set of frequency scaling factors is the set that gives the highest distance according to  the objective function EQ(\ref{eq:max}).
-
-  
-
+In  figure (\ref{fig:st_freq}), the nodes are  sorted by their computing powers in ascending order and the frequencies of the faster nodes are scaled down according to the computed initial frequency scaling factors. The resulting new frequencies are coloured in blue in  figure (\ref{fig:st_freq}). This set of frequencies can be considered as a higher bound for the search space of the optimal set of frequencies because selecting frequency scaling factors higher than the higher bound will not improve the performance of the application and it will increase its overall energy consumption. Therefore the frequency selecting factors algorithm starts its search method from these initial frequencies and takes a downward search direction. The algorithm iterates on all left frequencies, from the higher bound until all nodes reach their minimum frequencies, to compute their overall energy consumption and performance, and select the optimal frequency scaling factors vector. At each iteration the algorithm determines the slowest node according to EQ(\ref{eq:perf}) and keeps its frequency unchanged, while it lowers the frequency of  all other nodes by one gear. The new overall energy consumption and execution time are computed according to the new scaling factors. The optimal set of frequency scaling factors is the set that gives the highest distance according to  the objective function EQ(\ref{eq:max}).
+\begin{figure}[t]
+  \centering
+    \includegraphics[scale=0.5]{fig/start_freq}
+  \caption{Selecting the initial frequencies}
+  \label{fig:st_freq}
+\end{figure}

 
 
 This algorithm has a small
 
 
 This algorithm has a small


@@ -352,19 +355,10 @@ nodes having the characteristics presented in table~(\ref{table:platform}), it
 takes \np[ms]{0.04} on average for 4 nodes and \np[ms]{0.15} on average for 144
 nodes.  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
 takes \np[ms]{0.04} on average for 4 nodes and \np[ms]{0.15} on average for 144
 nodes.  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 on average from 12 to 20 iterations to selects the best vector of frequency scaling factors that give the results of the next section. 
+needs on average from 12 to 20 iterations to selects the best vector of frequency scaling factors that give the results of the next section. \textbf{put the lst paragraph in experiments}
+

 
 
 
 

-Therefore, there is a small distance between the energy and
-the performance curves in a homogeneous cluster compare to heterogeneous one, for example see the figure(\ref{fig:r1}) and figure(\ref{fig:r2}) .  Then the
-algorithm starts to search for the optimal vector of the frequency scaling factors from the selected initial 
-frequencies until all node reach their minimum frequencies.
-\begin{figure}[t]
-  \centering
-    \includegraphics[scale=0.5]{fig/start_freq}
-  \caption{Selecting the initial frequencies}
-  \label{fig:st_freq}
-\end{figure}