Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/hpcc2014

[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 8bf89cd6f88d04b75097846dd45e769678759a40..c79ed41db32a4a2874f133a3131b97d14781a202 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -395,9 +395,9 @@ processor is designated (for example the processor with rank 1) and masters of
 all clusters are interconnected by a virtual unidirectional ring network (see
 Figure~\ref{fig:4.1}). During the resolution, a Boolean token circulates around
 the virtual ring from a master processor to another until the global convergence
 all clusters are interconnected by a virtual unidirectional ring network (see
 Figure~\ref{fig:4.1}). During the resolution, a Boolean token circulates around
 the virtual ring from a master processor to another until the global convergence

-is achieved. So starting from the cluster with rank 1, each master processor $i$
+is achieved. So starting from the cluster with rank 1, each master processor $\ell$

 sets the token to \textit{True} if the local convergence is achieved or to
 sets the token to \textit{True} if the local convergence is achieved or to

-\textit{False} otherwise, and sends it to master processor $i+1$. Finally, the
+\textit{False} otherwise, and sends it to master processor $\ell+1$. Finally, the

 global convergence is detected when the master of cluster 1 receives from the
 master of cluster $L$ a token set to \textit{True}. In this case, the master of
 cluster 1 broadcasts a stop message to masters of other clusters. In this work,
 global convergence is detected when the master of cluster 1 receives from the
 master of cluster $L$ a token set to \textit{True}. In this case, the master of
 cluster 1 broadcasts a stop message to masters of other clusters. In this work,


@@ -476,15 +476,14 @@ study that the results depend on the following parameters:
 \item Hosts processors power (GFlops) can also influence on the results.
 \item Finally, when submitting job batches for execution, the arguments values
   passed to the program like the maximum number of iterations or the precision are critical. They allow us to ensure not only the convergence of the
 \item Hosts processors power (GFlops) can also influence on the results.
 \item Finally, when submitting job batches for execution, the arguments values
   passed to the program like the maximum number of iterations or the precision are critical. They allow us to ensure not only the convergence of the

-  algorithm but also to get the main objective in getting an execution time in asynchronous communication less than in
-  synchronous mode. The ratio between the simulated execution time of synchronous GMRES algorithm
-  compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
-  our objective running the algorithm in SimGrid is to obtain a relative gain
-  greater than 1.
-\end{itemize}
+  algorithm but also to get the main objective in getting an execution time with the asynchronous multisplitting  less than with synchronous GMRES. 
+  \end{itemize}

 
 

+The ratio between the simulated execution time of synchronous GMRES algorithm
+compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
+our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1.

 A priori, obtaining a relative gain greater than 1 would be difficult in a local
 A priori, obtaining a relative gain greater than 1 would be difficult in a local

-area network configuration where the synchronous mode will take advantage on the
+area network configuration where the synchronous GMRES method will take advantage on the

 rapid exchange of information on such high-speed links. Thus, the methodology
 adopted was to launch the application on a clustered network. In this
 configuration, degrading the inter-cluster network performance will penalize the
 rapid exchange of information on such high-speed links. Thus, the methodology
 adopted was to launch the application on a clustered network. In this
 configuration, degrading the inter-cluster network performance will penalize the


@@ -509,7 +508,8 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
 
 \begin{table}[!t]
   \centering
 
 \begin{table}[!t]
   \centering

-  \caption{2 clusters, each with 50 nodes}
+  \caption{Relative gain  of the multisplitting algorithm compared  to GMRES for
+    different configurations with 2 clusters, each one composed of 50 nodes.}

   \label{tab.cluster.2x50}
 
   \begin{mytable}{5}
   \label{tab.cluster.2x50}
 
   \begin{mytable}{5}


@@ -630,13 +630,12 @@ Note that the program was run with the following parameters:
 
 \begin{itemize}
 \item HOSTFILE: Text file containing the list of the processors units name. Here 100 hosts;
 
 \begin{itemize}
 \item HOSTFILE: Text file containing the list of the processors units name. Here 100 hosts;

-\item PLATFORM: XML file description of the platform architecture : two clusters (cluster1 and cluster2) with the following characteristics :
+\item PLATFORM: XML file description of the platform architecture whith the following characteristics: %two clusters (cluster1 and cluster2) with the following characteristics :

   \begin{itemize}
   \begin{itemize}

-  \item Processor unit power: \np[GFlops]{1.5};
-  \item Intracluster network bandwidth: \np[Gbit/s]{1.25} and latency:
-    \np[$\mu$s]{0.05};
-  \item Intercluster network bandwidth: \np[Mbit/s]{5} and latency:
-    \np[$\mu$s]{5};
+  \item 2 clusters of 50 hosts each;
+  \item Processor unit power: \np[GFlops]{1} or \np[GFlops]{1.5};
+  \item Intra-cluster network bandwidth: \np[Gbit/s]{1.25} and latency: \np[$\mu$s]{0.05};
+  \item Inter-cluster network bandwidth: \np[Mbit/s]{5} or \np[Mbit/s]{50} and latency: \np[$\mu$s]{20};

   \end{itemize}
 \end{itemize}
 
   \end{itemize}
 \end{itemize}
 


@@ -645,11 +644,11 @@ Note that the program was run with the following parameters:
 
 \begin{itemize}
 \item Description of the cluster architecture matching the format <Number of
 
 \begin{itemize}
 \item Description of the cluster architecture matching the format <Number of

-  cluster> <Number of hosts in cluster1> <Number of hosts in cluster2>;
+  clusters> <Number of hosts in cluster1> <Number of hosts in cluster2>;

 \item Maximum number of iterations;
 \item Precisions on the residual error;
 \item Matrix size $N_x$, $N_y$ and $N_z$;
 \item Maximum number of iterations;
 \item Precisions on the residual error;
 \item Matrix size $N_x$, $N_y$ and $N_z$;

-\item Matrix diagonal value: $6$ (See~(\ref{eq:03}));
+\item Matrix diagonal value: $6$ (See Equation~(\ref{eq:03}));

 \item Matrix off-diagonal value: $-1$;
 \item Communication mode: asynchronous.
 \end{itemize}
 \item Matrix off-diagonal value: $-1$;
 \item Communication mode: asynchronous.
 \end{itemize}


@@ -658,10 +657,10 @@ Note that the program was run with the following parameters:
 
 After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
 the results have given a relative gain more than 2.5, showing the effectiveness of the
 
 After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
 the results have given a relative gain more than 2.5, showing the effectiveness of the

-asynchronous performance compared to the synchronous mode.
+asynchronous multisplitting  compared to GMRES with two distant clusters.

 
 With these settings, Table~\ref{tab.cluster.2x50} shows
 
 With these settings, Table~\ref{tab.cluster.2x50} shows

-that after a deterioration of inter cluster network with a bandwidth of \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
+that after setting the bandwidth of the  inter cluster network to  \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power

 of one GFlops, an efficiency of about \np[\%]{40} is
 obtained in asynchronous mode for a matrix size of 62 elements. It is noticed that the result remains
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By
 of one GFlops, an efficiency of about \np[\%]{40} is
 obtained in asynchronous mode for a matrix size of 62 elements. It is noticed that the result remains
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By


@@ -691,10 +690,8 @@ elements.
 %\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??}
 %\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau INTER cluster.}
 \section{Conclusion}
 %\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??}
 %\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau INTER cluster.}
 \section{Conclusion}

-The experimental results on executing a parallel iterative algorithm in 
-asynchronous mode on an environment simulating a large scale of virtual 
-computers organized with interconnected clusters have been presented. 
-Our work has demonstrated that using such a simulation tool allow us to 
+The simulation of the execution of parallel asynchronous iterative algorithms on large scale  clusters has been presented. 
+In this work, we show that SIMGRID is an efficient simulation tool that allows us to 

 reach the following three objectives: 
 
 \begin{enumerate}
 reach the following three objectives: 
 
 \begin{enumerate}


@@ -708,22 +705,23 @@ of the cluster and network specifications permitting to save time in
 executing the algorithm in asynchronous mode.
 \end{enumerate}
 Our results have shown that in certain conditions, asynchronous mode is 
 executing the algorithm in asynchronous mode.
 \end{enumerate}
 Our results have shown that in certain conditions, asynchronous mode is 

-speeder up to \np[\%]{40} than executing the algorithm in synchronous mode
+speeder up to \np[\%]{40} comparing to the synchronous GMRES method

 which is not negligible for solving complex practical problems with more 
 and more increasing size.
 
 which is not negligible for solving complex practical problems with more 
 and more increasing size.
 

- Several studies have already addressed the performance execution time of 
+Several studies have already addressed the performance execution time of 

 this class of algorithm. The work presented in this paper has 
 demonstrated an original solution to optimize the use of a simulation 
 tool to run efficiently an iterative parallel algorithm in asynchronous 
 mode in a grid architecture. 
 
 this class of algorithm. The work presented in this paper has 
 demonstrated an original solution to optimize the use of a simulation 
 tool to run efficiently an iterative parallel algorithm in asynchronous 
 mode in a grid architecture. 
 

-\LZK{Perspectives???}
+For our futur works, we plan to extend our experimentations to larger scale platforms by increasing the number of computing cores and the number of clusters. 
+We will also have to increase the size of the input problem which will require the use of a more powerful simulation platform. At last, we expect to compare our simulation results to real execution results on real architectures in order to experimentally validate our study.

 
 \section*{Acknowledgment}
 
 This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
 
 \section*{Acknowledgment}
 
 This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).

-\todo[inline]{The authors would like to thank\dots{}}
+%\todo[inline]{The authors would like to thank\dots{}}

 
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