\section{Introduction}
\label{sec.intro}
Modern processors continue to increased in a performance, achieved maximum number of floating point operations per second (FLOPS), thus the energy consumption and the heat dissipation are increased drastically according to this increase. The number of FLOPS is linearly related to power consumption of a CPU~\cite{51}.
-As an example of more power hungry cluster, according to the Top500 list in June 2014 \cite{43}, Tianhe-2 has more than 3 millions of cores and consumed more than 17.8 megawatt per second. Moreover, according to the U.S. annual energy outlook 2014 \cite{60}, the price of energy for 1 megawatt per hour is approximately equal to 70\$ (1.16\$ for megawatt per second). Therefore, we can consider the price of the energy consumption for the Tianhe-2 platform is approximately more than 390 millions dollars of megawatt per year. For this reason, the heterogeneous clusters must be offer more energy efficiency due to the increase in the energy cost and the environment influences. Therefore, a green computing clusters are require nowadays. For example, the GSIC center of Tokyo heterogeneous cluster became the top of the Green500 list in June 2014 \cite{59}. This platform has more than four thousand of MFLOPS per watt. Dynamic voltage and frequency scaling (DVFS) is a process used widely to reduce the energy consumption of the processor. In a heterogeneous clusters enabled DVFS, many researchers used DVFS in a different ways. DVFS can be minimized the energy consumption but it lead to a disadvantage due to the performance degradation increase. Therefore, researchers used different optimization strategies to overcame this problem. The best tradeoff relation between the energy reduction and performance degradation ratio is become a key challenges in a heterogeneous platforms. In this paper we are propose a heterogeneous scaling algorithm that selects the optimal vector of the frequency scaling factors for distributed iterative application, producing minimum energy saving against minimum performance degradation ratio simultaneously. The algorithm has very small overhead, works online and not needs for any training or profiling.
+As an example of more power hungry cluster, according to the Top500 list in June 2014 \cite{43}, Tianhe-2 has more than 3 millions of cores and consumed more than 17.8 megawatt per second. Moreover, according to the U.S. annual energy outlook 2014 \cite{60}, the price of energy for 1 megawatt per hour is approximately equal to 70\$ (1.16\$ for megawatt per second). Therefore, we can consider the price of the energy consumption for the Tianhe-2 platform is approximately more than 390 millions dollars of megawatt per year. For this reason, the heterogeneous clusters must be offer more energy efficiency due to the increase in the energy cost and the environment influences. Therefore, a green computing clusters with maximum number of FLOPS per watt are required nowadays. For example, the GSIC center of Tokyo heterogeneous cluster became the top of the Green500 list in June 2014 \cite{59}. This platform has more than four thousand of MFLOPS per watt. Dynamic voltage and frequency scaling (DVFS) is a process used widely to reduce the energy consumption of the processor. In a heterogeneous clusters enabled DVFS, many researchers used DVFS in a different ways. DVFS can be minimized the energy consumption but it leads to a disadvantage due to increase in performance degradation. Therefore, researchers used different optimization strategies to overcame this problem. The best tradeoff relation between the energy reduction and performance degradation ratio is became a key challenges in a heterogeneous platforms. In this paper we are propose a heterogeneous scaling algorithm that selects the optimal vector of the frequency scaling factors for distributed iterative application, producing minimum energy saving against minimum performance degradation ratio simultaneously. The algorithm has very small overhead, works online and not needs for any training or profiling.
This paper is organized as follows: Section~\ref{sec.relwork} presents some
related works from other authors. Section~\ref{sec.exe} describes how the
