-Energy reduction process for a high performance clusters recently performed using dynamic voltage and frequency scaling (DVFS) technique. DVFS is a technique enabled in a modern processors to scaled down both of the voltage and the frequency of the CPU while it is in the computing mode to reduce the energy consumption. DVFS is also allowed in the graphical processors GPUs, to achieved the same goal. Applying DVFS has a dramatical side effect if it is applied to minimum levels to gain more energy reduction, producing a high percentage of performance degradations for the parallel applications. Many researchers used different strategies to solve this nonlinear problem for example 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 for a heterogeneous cluster to simultaneously optimize both the energy and the execution time without adding a big overhead.
-This work is developed from our previous work of a homogeneous cluster~\cite{45}. Therefore we are interested to present some works that concerned the heterogeneous clusters enabled DVFS. In general, the heterogeneous cluster works fall into two categorizes: GPUs-CPUs heterogeneous clusters and CPUs-CPUs heterogeneous clusters. In GPUs-CPUs heterogeneous clusters some parallel tasks executed on a GPUs and the others executed on a CPUs. As an example of this works, Luley et al.~\cite{51}, proposed a heterogeneous cluster composed of Intel Xeon CPUs and NVIDIA GPUs. Their main goal is to determined the energy efficiency as a function of performance per watt, the best tradeoff is done when the performance per watt function is maximized. In the work of Kia Ma et al.~\cite{49}, They developed a scheduling algorithm to distribute different workloads proportional to the computing power of the node to be executed on a CPU or a GPU, emphasize all tasks must be finished in the same time.
-Recently, Rong et al.~\cite{50}, Their study explain that a heterogeneous clusters enabled DVFS using GPUs and CPUs gave better energy and performance efficiency
-than other clusters composed of only CPUs. The CPUs-CPUs heterogeneous clusters consist of number of computing nodes all of the type CPU. Our work in this paper can be classified to this type of the clusters. As an example of this works see Naveen et al.~\cite{52} work, They developed a policy to dynamically assigned the frequency to a heterogeneous cluster. The goal is to minimizing a fixed metric of $energy*delay^2$. Where our proposed method is automatically optimized the relation between the energy and the delay of the iterative applications. Other works such as Lizhe et al.~\cite{53}, their algorithm divided the executed tasks into two types: the critical and non critical tasks. The algorithm scaled down the frequency of the non critical tasks as function to the amount of the slack and communication times that have with maximum of performance degradation percentage of 10\%. In our method there is no fixed bounds for performance degradation percentage and the bound is dynamically computed according to the energy and the performance tradeoff relation of the executed application.
-There are some approaches used a heterogeneous cluster composed from two different types of Intel and AMD processors such as~\cite{54} and \cite{55}, they predicated both the energy and the performance for each frequency gear, then the algorithm selected the best gear that gave the best tradeoff. In contrast our algorithm works over a heterogeneous platform composed of four different types of processors. Others approaches such as \cite{56} and \cite{57}, they are selected the best frequencies for a specified heterogeneous clusters offline using some heuristic methods. While our proposed algorithm works online during the execution time of iterative application. Greedy dynamic approach used by Chen et al.~\cite{58}, minimized the power consumption of a heterogeneous severs with time/space complexity, this approach had considerable overhead. In our proposed scaling algorithm has very small overhead and it is works without any previous analysis for the application time complexity.
+Energy reduction process for a high performance clusters recently performed using
+dynamic voltage and frequency scaling (DVFS) technique. DVFS is a technique enabled
+in a modern processors to scaled down both of the voltage and the frequency of
+the CPU while it is in the computing mode to reduce the energy consumption. DVFS is
+also allowed in the graphical processors GPUs, to achieved the same goal. Applying
+DVFS has a dramatical side effect if it is applied to minimum levels to gain more
+energy reduction, producing a high percentage of performance degradations for the
+parallel applications. Many researchers used different strategies to solve this
+nonlinear problem for example in
+~\cite{Hao_Learning.based.DVFS,Dhiman_Online.Learning.Power.Management}, 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 for a heterogeneous cluster to
+simultaneously optimize both the energy and the execution time without adding a big
+overhead. This work is developed from our previous work of a homogeneous cluster~\cite{Our_first_paper}.
+Therefore we are interested to present some works that concerned the heterogeneous clusters
+enabled DVFS. In general, the heterogeneous cluster works fall into two categorizes:
+GPUs-CPUs heterogeneous clusters and CPUs-CPUs heterogeneous clusters. In GPUs-CPUs
+heterogeneous clusters some parallel tasks executed on a GPUs and the others executed
+on a CPUs. As an example of this works, Luley et al.
+~\cite{Luley_Energy.efficiency.evaluation.and.benchmarking}, proposed a heterogeneous
+cluster composed of Intel Xeon CPUs and NVIDIA GPUs. Their main goal is to determined the
+energy efficiency as a function of performance per watt, the best tradeoff is done when the
+performance per watt function is maximized. In the work of Kia Ma et al.
+~\cite{KaiMa_Holistic.Approach.to.Energy.Efficiency.in.GPU-CPU}, They developed a scheduling
+algorithm to distributed different workloads proportional to the computing power of the node
+to be executed on a CPU or a GPU, emphasize all tasks must be finished in the same time.
+Recently, Rong et al.~\cite{Rong_Effects.of.DVFS.on.K20.GPU}, Their study explain that
+a heterogeneous clusters enabled DVFS using GPUs and CPUs gave better energy and performance
+efficiency than other clusters composed of only CPUs.
+The CPUs-CPUs heterogeneous clusters consist of number of computing nodes all of the type CPU.
+Our work in this paper can be classified to this type of the clusters.
+As an example of this works see Naveen et al.~\cite{Naveen_Power.Efficient.Resource.Scaling} work,
+They developed a policy to dynamically assigned the frequency to a heterogeneous cluster.
+The goal is to minimizing a fixed metric of $energy*delay^2$. Where our proposed method is automatically
+optimized the relation between the energy and the delay of the iterative applications.
+Other works such as Lizhe et al.~\cite{Lizhe_Energy.aware.parallel.task.scheduling},
+their algorithm divided the executed tasks into two types: the critical and
+non critical tasks. The algorithm scaled down the frequency of the non critical tasks
+as function to the amount of the slack and communication times that
+have with maximum of performance degradation percentage of 10\%. In our method there is no
+fixed bounds for performance degradation percentage and the bound is dynamically computed
+according to the energy and the performance tradeoff relation of the executed application.
+There are some approaches used a heterogeneous cluster composed from two different types
+of Intel and AMD processors such as~\cite{Joshi_Blackbox.prediction.of.impact.of.DVFS}
+and \cite{Spiliopoulos_Green.governors.Adaptive.DVFS}, they predicated both the energy
+and the performance for each frequency gear, then the algorithm selected the best gear that gave
+the best tradeoff. In contrast our algorithm works over a heterogeneous platform composed of
+four different types of processors. Others approaches such as
+\cite{Shelepov_Scheduling.on.Heterogeneous.Multicore} and \cite{Li_Minimizing.Energy.Consumption.for.Frame.Based.Tasks},
+they are selected the best frequencies for a specified heterogeneous clusters offline using some
+heuristic methods. While our proposed algorithm works online during the execution time of
+iterative application. Greedy dynamic approach used by Chen et al.~\cite{Chen_DVFS.under.quality.of.service.requirements},
+minimized the power consumption of a heterogeneous severs with time/space complexity, this approach
+had considerable overhead. In our proposed scaling algorithm has very small overhead and
+it is works without any previous analysis for the application time complexity.
