X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/e3eaeb5f6e4963220fa7da4ba4afec74c5727833..b69bcefdfa54757425b8e8ffd4a807d02d1225c1:/hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 81062de..306cf68 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -82,8 +82,8 @@ what parameters  could influence or not  the behaviors of an  algorithm. In this
 paper, we show  that it is interesting to use SimGrid  to simulate the behaviors
 of asynchronous  iterative algorithms. For that,  we compare the  behaviour of a
 synchronous  GMRES  algorithm  with  an  asynchronous  multisplitting  one  with
-simulations  in  which we  choose  some parameters.   Both  codes  are real  MPI
-codes. Simulations allow us to see when the multisplitting algorithm can be more
+simulations  which let us easily choose  some parameters.   Both  codes  are real  MPI
+codes and simulations allow us to see when the asynchronous multisplitting algorithm can be more
 efficient than the GMRES one to solve a 3D Poisson problem.
 
 
@@ -144,11 +144,11 @@ execution time.
 
 To our knowledge,  there is no existing work on the  large-scale simulation of a
 real asynchronous  iterative application.  {\bf The contribution  of the present
-  paper can be  summarised in two main points}.  First we  give a first approach
+  paper can be  summarized in two main points}.  First we  give a first approach
 of the simulation  of asynchronous iterative algorithms using  a simulation tool
 (i.e.    the   SimGrid   toolkit~\cite{SimGrid}).    Second,  we   confirm   the
 effectiveness  of the  asynchronous  multisplitting algorithm  by comparing  its
-performance   with  the   synchronous  GMRES   (Generalized   Minimal  Residual)
+performance   with  the   synchronous  GMRES   (Generalized   Minimal  Residual) method
 \cite{ref1}.  Both  these codes can  be used to  solve large linear  systems. In
 this  paper, we  focus  on  a 3D  Poisson  problem.  We  show,  that with  minor
 modifications of the initial MPI code,  the SimGrid toolkit allows us to perform
@@ -288,6 +288,8 @@ These two techniques can help to run simulations at a very large scale.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}
+
+\subsection{The multisplitting method}
 %DÃ©crire le problÃ¨me (algo) traitÃ© ainsi que le processus d'adaptation Ã  SimGrid.
 Let $Ax=b$ be a large sparse system of $n$ linear equations in $\mathbb{R}$, where $A$ is a sparse square and nonsingular matrix, $x$ is the solution vector and $b$ is the right-hand side vector. We use a multisplitting method based on the block Jacobi splitting to solve this linear system on a large scale platform composed of $L$ clusters of processors~\cite{o1985multi}. In this case, we apply a row-by-row splitting without overlapping  
 \begin{equation*}
@@ -381,8 +383,8 @@ exchanged by message passing using MPI non-blocking communication routines.
 
 \begin{figure}[!t]
 \centering
-  \includegraphics[width=60mm,keepaspectratio]{clustering}
-\caption{Example of three clusters of processors interconnected by a virtual unidirectional ring network.}
+  \includegraphics[width=60mm,keepaspectratio]{clustering2}
+\caption{Example of two distant clusters of processors.}
 \label{fig:4.1}
 \end{figure}
 
@@ -393,9 +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
-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
-\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,
@@ -442,13 +444,14 @@ The parallel solving of the 3D Poisson problem with our multisplitting method re
 \end{figure}
 
 
+\subsection{Simulation of the multisplitting method using SimGrid and SMPI}
+
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 We did not encounter major blocking problems when adapting the multisplitting algorithm previously described to a simulation environment like SimGrid unless some code 
-debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between processors within a cluster or between clusters, the algorithm was executed successfully with SMPI and provided identical outputs as those obtained with direct execution under MPI. In synchronous 
-mode, the execution of the program raised no particular issue but in asynchronous mode, the review of the sequence of MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions
-and with the addition of the primitive MPI\_Test was needed to avoid a memory fault due to an infinite loop resulting from the non-convergence of the algorithm.
+debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between processors within a cluster or between clusters, the algorithm was executed successfully with SMPI and provided identical outputs as those obtained with direct execution under MPI. For the synchronous GMRES method, the execution of the program raised no particular issue but in the asynchronous multisplitting method , the review of the sequence of \texttt{MPI\_Isend, MPI\_Irecv} and \texttt{MPI\_Waitall} instructions
+and with the addition of the primitive \texttt{MPI\_Test} was needed to avoid a memory fault due to an infinite loop resulting from the non-convergence of the algorithm.
 %\CER{On voulait en fait montrer la simplicitÃ© de l'adaptation de l'algo a SimGrid. Les problÃ¨mes rencontrÃ©s dÃ©crits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais prÃ©fÃ©rÃ© avoir un peu plus de dÃ©tails sur l'adaptation de la version async} 
 %\CER{Le problÃ¨me majeur sur l'adaptation MPI vers SMPI pour la partie asynchrone de l'algorithme a Ã©tÃ© le plantage en SMPI de Waitall aprÃ¨s un Isend et Irecv. J'avais proposÃ© un workaround en utilisant un MPI\_wait sÃ©parÃ© pour chaque Ã©change a la place d'un waitall unique pour TOUTES les Ã©changes, une instruction qui semble bien fonctionner en MPI. Ce workaround aussi fonctionne bien. Mais aprÃ¨s, tu as modifiÃ© le programme avec l'ajout d'un MPI\_Test, au niveau de la routine de dÃ©tection de la convergence et du coup, l'Ã©change global avec waitall a aussi fonctionnÃ©.}
 Note here that the use of SMPI functions optimizer for memory footprint and CPU usage is not recommended knowing that one wants to get real results by simulation.
@@ -458,7 +461,7 @@ shared memory used by threads simulating each computing unit in the SimGrid arch
 %Second, some compilation errors on MPI\_Waitall and MPI\_Finalize primitives have been fixed with the latest version of SimGrid.
 %\AG{compilation or run-time error?}
 In total, the initial MPI program running on the simulation environment SMPI gave after a very simple adaptation the same results as those obtained in a real 
-environment. We have successfully executed the code in synchronous mode using parallel GMRES algorithm compared with our multisplitting algorithm in asynchronous mode after few modifications. 
+environment. We have successfully executed the code for the synchronous GMRES algorithm compared with our asynchronous multisplitting algorithm after few modifications. 
 
 
 
@@ -473,15 +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
-  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
-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
@@ -506,7 +508,8 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
 
 \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}
@@ -515,7 +518,7 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
     & 5         & 5         & 5         & 5         & 5         \\
     \hline
     latency (ms)
-    & 0.02      & 0.02      & 0.02      & 0.02      & 0.02      \\
+    & 20      &  20      & 20      & 20      & 20      \\
     \hline
     power (GFlops)
     & 1         & 1         & 1         & 1.5       & 1.5       \\
@@ -540,7 +543,7 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
     & 50        & 50        & 50        & 50        & 50 \\ %       & 10        & 10 \\
     \hline
     latency (ms)
-    & 0.02      & 0.02      & 0.02      & 0.02      & 0.02 \\ %      & 0.03      & 0.01 \\
+    & 20      & 20      & 20      & 20      & 20 \\ %      & 0.03      & 0.01 \\
     \hline
     Power (GFlops)
     & 1.5       & 1.5       & 1.5       & 1.5       & 1.5 \\ %      & 1         & 1.5 \\
@@ -558,13 +561,15 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
   \end{mytable}
 \end{table}
   
+\RC{Du coup la latence est toujours la mÃªme, pourquoi la mettre dans la table?}
+
 %Then we have changed the network configuration using three clusters containing
 %respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the
 %clusters. In the same way as above, a judicious choice of key parameters has
 %permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the
 %relative gains greater than 1 with a matrix size from 62 to 100 elements.
 
-\CER{En accord avec RC, on a pour le moment enlevÃ© les tableaux 2 et 3 sachant que les rÃ©sultats obtenus sont limites. De mÃªme, on a enlevÃ© aussi les deux derniÃ¨res colonnes du tableau I en attendant une meilleure performance et une meilleure precision}
+%\CER{En accord avec RC, on a pour le moment enlevÃ© les tableaux 2 et 3 sachant que les rÃ©sultats obtenus sont limites. De mÃªme, on a enlevÃ© aussi les deux derniÃ¨res colonnes du tableau I en attendant une meilleure performance et une meilleure precision}
 %\begin{table}[!t]
 %  \centering
 %  \caption{3 clusters, each with 33 nodes}
@@ -627,13 +632,12 @@ 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;
-\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}
-  \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]{50};
+  \item Inter-cluster network bandwidth: \np[Mbit/s]{5} or \np[Mbit/s]{50} and latency: \np[ms]{20};
   \end{itemize}
 \end{itemize}
 
@@ -642,11 +646,11 @@ Note that the program was run with the following parameters:
 
 \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 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}
@@ -655,10 +659,10 @@ 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
-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
-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
@@ -688,39 +692,35 @@ elements.
 %\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??}
 %\CER{DÃ©finitivement, les paramÃ¨tres rÃ©seaux variables ici se rapportent au rÃ©seau 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 
-reach the following three objectives: 
+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 two objectives: 
 
 \begin{enumerate}
-\item To have a flexible configurable execution platform resolving the 
-hard exercise to access to very limited but so solicited physical 
-resources;
-\item to ensure the algorithm convergence with a reasonable time and
-iteration number ;
-\item and finally and more importantly, to find the correct combination 
-of the cluster and network specifications permitting to save time in 
-executing the algorithm in asynchronous mode.
+\item  To have  a flexible  configurable execution  platform that  allows  us to
+  simulate algorithms for  which execution of all parts of
+  the  code is  necessary. Using  simulations before  real executions  is  a nice
+  solution to detect potential scalability problems.
+
+\item To test the combination of the cluster and network specifications permitting to execute an asynchronous algorithm faster than a synchronous one.
 \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
+Our results have shown that with two distant clusters, the asynchronous multisplitting is faster to \np[\%]{40} compared to the synchronous GMRES method
 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. 
 
-\LZK{Perspectives???}
+In future 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).
-\todo[inline]{The authors would like to thank\dots{}}
+%\todo[inline]{The authors would like to thank\dots{}}
 
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