-In this section we are proposed a heterogeneous scaling algorithm,
-(figure~\ref{HSA}), that selects the optimal vector of the frequency scaling factors from each
-node. The algorithm is numerates the suitable range of available frequency scaling
-factors for each node in a heterogeneous cluster, returns a vector of optimal
-frequency scaling factors for all node define as $Sopt_1,Sopt_2,\dots,Sopt_N$. Using heterogeneous cluster
-has different computing powers is produces different workloads for each node. Therefore, the fastest nodes waiting at the
-synchronous barrier for the slowest nodes to finish there work as in figure
-(\ref{fig:heter}). Our algorithm is takes into account these imbalanced workloads
-when is starts to search for selecting the best vector of the frequency scaling factors. So, the
-algorithm is selects the initial frequencies values for each node proportional
-to the times of computations that gathered from the first iteration. As an
-example in figure (\ref{fig:st_freq}), the algorithm don't tests the first
-frequencies of the computing nodes until it is converge their frequencies to the
-frequency of the slowest node. If the algorithm is starts to test changing the
-frequency of the slowest node from the first gear, we are loosing the performance and
-then the best trade-off relation (the maximum distance) be not reachable. This case will be similar
-to a homogeneous cluster when all nodes scales their frequencies together from
-the first gear. 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}). 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}
