\subsection{The comparison of the proposed frequencies selecting algorithm }
\label{sec.compare_EDP}
+The tradeoff between the energy consumption and the performance of the parallel
+application had significant importance in the domain of the research.
+Many researchers, \cite{EDP_for_multi_processors,Energy_aware_application_scheduling,Exploring_Energy_Performance_TradeOffs},
+are optimized the tradeoff between the energy and performance using the energy and delay product, $EDP=energy \times delay$.
+This model is used by Spiliopoulos et al. algorithm \cite{Spiliopoulos_Green.governors.Adaptive.DVFS},
+the objective is to selects the suitable frequencies that minimized EDP product for the multicores
+architecture when DVFS is used. Moreover, their algorithm is applied online which synchronously optimized the energy consumption
+and the execution time. Both energy consumption and execution time of a processor are predicted by the their algorithm.
+In this section the proposed frequency selection algorithm, called Maxdist is compared with Spiliopoulos et al. algorithm, called EDP.
+To make both of the algorithms follow the same direction and fairly comparing them, the same energy model, equation \ref{eq:energy} and
+the execution time model, equation \ref{eq:perf}, are used in the prediction process to select the best vector of the frequencies.
+In contrast, the proposed algorithm starts the search space from the lower bound computed as in equation the \ref{eq:Fint}. Also, the algorithm
+stops the search process when reaching to the lower bound as mentioned before. While, the EDP algorithm is developed to start from the
+same upper bound until it reach to the minimum available frequencies. Finally, resulting the algorithm is an exhaustive search algorithm that
+test all possible frequencies, starting from the initial frequencies, and selecting those minimized the EDP products.
+
+Both algorithms were applied to NAS benchmarks class D over 16 nodes selected from grid'5000 clusters.
+The participating computing nodes are distributed between two sites to had two different scenarios.
+These scenarios are two sites and one site scenarios that explained previously.
+The experimental results of the energy saving, performance degradation and tradeoff distance are
+presented in the figures \ref{fig:edp-eng}, \ref{fig:edp-perf} and \ref{fig:edp-dist} respectively.
+
+In one site scenario the proposed frequencies selection algorithm outperform the EDP algorithm
+in term of energy and performance for all of the benchmarks. While, the compassion results from the two sites scenario
+showed that the proposed algorithm outperform EDP algorithm for all benchmarks except MG benchmark.
+In case of MG benchmark the are small communications and bigger frequencies selected in EDP algorithm
+decreased the performance degradation more than the frequencies selected by Maxdist algorithm.
+While the energy saving percentage are higher for Maxdist algorithm.
+
+Generally, the proposed algorithm gives better results for all benchmarks because it
+optimized the distance between the energy saving and the performance degradation.
+Whereas, in EDP algorithm gives negative tradeoff for some benchmarks in the two sites scenarios.
+These negative tradeoffs mean the performance degradation percentage is higher than energy saving percentage.
+The higher positive value for tradeoff distance is mean the best energy and performance tradeoff is achieved synchronously, when
+the energy saving percentage is much higher than the performance degradation percentage
+The time complexity of the proposed algorithm is $O(N \cdot M \cdot F)$, where $N$ is the number of the clusters,
+$M$ is the number of nodes and $F$ is the maximum number of available frequencies. The algorithm is selected
+the best frequencies in small execution time, on average is equal to 0.01 $ms$ when it works over 32 nodes.
+While the EDP algorithm was slower than Maxdist algorithm by ten times, where their execution time on average
+takes 0.1 $ms$ to selects the suitable frequencies over 32 nodes.
+The time complexity of this algorithm is $O(N^2 \cdot M^2 \cdot F)$.
+
+
+
+
+
+
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_eng}
+ \caption{Comparing of the energy saving for the proposed method with EDP method}
+ \label{fig:edp-eng}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_per}
+ \caption{Comparing of the performance degradation for the proposed method with EDP method}
+ \label{fig:edp-perf}
+\end{figure}
+
+\begin{figure}
+ \centering
+ \includegraphics[scale=0.5]{fig/edp_dist}
+ \caption{Comparing of the tradeoff distance for the proposed method with EDP method}
+ \label{fig:edp-dist}
+\end{figure}
\section{Conclusion}
year={2013},
publisher={Springer Science \& Business Media}
}
+
+@article{EDP_for_multi_processors,
+year={2015},
+journal={Human-centric Computing and Information Sciences},
+eid={28},
+volume={5},
+number={1},
+doi={10.1186/s13673-015-0046-x},
+title={An energy-delay product study on chip multi-processors for variable stage pipelining},
+url={http://dx.doi.org/10.1186/s13673-015-0046-x},
+publisher={Springer Berlin Heidelberg},
+keywords={Chip multi-processors (CMP); Variable stage pipelining (VSP); Power-performance; Optimal pipeline},
+author={Saravanan, Vijayalakshmi and Anpalagan, Alagan and Woungang, Isaac}
+}
+
+
+@INPROCEEDINGS{Energy_aware_application_scheduling,
+author={Jian Chen and John, L.K.},
+booktitle={Workload Characterization, 2008. IISWC 2008. IEEE International Symposium on},
+title={Energy-aware application scheduling on a heterogeneous multi-core system},
+year={2008},
+pages={5-13},
+keywords={fuzzy logic;power aware computing;processor scheduling;resource allocation;branch transition rate;energy-aware application scheduling mechanism;fuzzy logic;heterogeneous multicore processor;instruction dependency distance;power efficient computing;program execution;random scheduling approach;resource requirement;suitability-guided program scheduling mechanism;workload balancing;Algorithm design and analysis;Application software;Energy consumption;Fuzzy logic;Hardware;Multicore processing;Power engineering and energy;Power engineering computing;Processor scheduling;Scheduling algorithm},
+doi={10.1109/IISWC.2008.4636086},
+month={Sept}
+}
+
+@INPROCEEDINGS{elusive_metric_for_low_power,
+ author = {Hsien-hsin S. Lee and Joshua B. Fryman and A. Utku Diril and Yuvraj S. Dhillon},
+ title = {The elusive metric for low-power architecture research},
+ booktitle = {In Proceedings of the Workshop on Complexity-Effective Design},
+ year = {2003}
+}
+
+@incollection{Exploring_Energy_Performance_TradeOffs,
+year={2006},
+isbn={978-3-540-68039-0},
+booktitle={High Performance Computing - HiPC 2006},
+volume={4297},
+editor={Robert, Yves and Parashar, Manish and Badrinath, Ramamurthy and Prasanna, ViktorK.},
+doi={10.1007/11945918_48},
+title={Exploring Energy-Performance Trade-Offs for Heterogeneous Interconnect Clustered VLIW Processors},
+url={http://dx.doi.org/10.1007/11945918_48},
+publisher={Springer Berlin Heidelberg},
+author={Nagpal, Rahul and Srikant, Y.N.},
+pages={497-508}
+}
