X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/64cf966afb9c408d8ab199f12a27f45e1c5ed82a..f2d52a8e01117d631783d873860e90d32f2bf8d5:/hpcc.tex?ds=sidebyside

diff --git a/hpcc.tex b/hpcc.tex
index d4dc19e..497ed68 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -68,7 +68,7 @@
 
 \maketitle
 
-\RC{Ordre des autheurs pas définitif.}
+\RC{Ordre des auteurs pas définitif.}
 \begin{abstract}
 In recent years, the scalability of large-scale implementation in a 
 distributed environment of algorithms becoming more and more complex has 
@@ -105,27 +105,27 @@ problems raised by  researchers on various scientific disciplines but also by in
 increasing complexity of these requested  applications combined with a continuous increase of their sizes lead to  write
 distributed and parallel algorithms requiring significant hardware  resources (grid computing, clusters, broadband
 network, etc.) but also a non-negligible CPU execution time. We consider in this paper a class of highly efficient
-parallel algorithms called \texttt{numerical iterative algorithms} executed in a distributed environment. As their name
+parallel algorithms called \emph{numerical iterative algorithms} executed in a distributed environment. As their name
 suggests, these algorithm solves a given problem by successive iterations ($X_{n +1} = f(X_{n})$) from an initial value
 $X_{0}$ to find an approximate value $X^*$ of the solution with a very low residual error. Several well-known methods
-demonstrate the convergence of these algorithms \cite{}. 
+demonstrate the convergence of these algorithms \cite{BT89,Bahi07}. 
 
 Parallelization of such algorithms generally involved the division of the problem into several \emph{blocks} that will
 be solved in parallel on multiple processing units. The latter will communicate each intermediate results before a new
 iteration starts and until the approximate solution is reached. These parallel  computations can be performed either in
 \emph{synchronous} mode where a new iteration begin only when all nodes communications are completed,
 either \emph{asynchronous} mode where processors can continue independently without or few synchronization points. For
-instance in the \textit{Asynchronous Iterations - Asynchronous   Communications (AIAC)} model \cite{bcvc06:ij}, local
+instance in the \textit{Asynchronous Iterations~-- Asynchronous Communications (AIAC)} model \cite{bcvc06:ij}, local
 computations do not need to wait for required data. Processors can then perform their iterations with the data present
 at that time. Even if the number of iterations required before the convergence is generally greater than for the
 synchronous case, AIAC algorithms can significantly reduce overall execution times by suppressing idle times due to
-synchronizations especially in a grid computing context (see \cite{bcvc06:ij} for more details).
+synchronizations especially in a grid computing context (see \cite{Bahi07} for more details).
 
 Parallel numerical applications (synchronous or asynchronous) may have different configuration and deployment
 requirements.  Quantifying their resource allocation policies and application scheduling algorithms in
 grid computing environments under varying load, CPU power and network speeds is very costly, very labor intensive and very time
-consuming \cite{BuRaCa}. The case of AIAC algorithms is even more problematic since they are very sensible to the
-execution environment context. For instance, variations in the network bandwith (intra and inter- clusters), in the
+consuming \cite{Calheiros:2011:CTM:1951445.1951450}. The case of AIAC algorithms is even more problematic since they are very sensible to the
+execution environment context. For instance, variations in the network bandwidth (intra and inter-clusters), in the
 number and the power of nodes, in the number of clusters... can lead to very different number of iterations and so to
 very different execution times. Then, it appears that the use of simulation tools to explore various platform
 scenarios and to run large numbers of experiments quickly can be very promising. In this way, the use of a simulation
@@ -141,7 +141,7 @@ paper is twofold. First we give a first approach of the simulation of AIAC algor
 SimGrid toolkit \cite{SimGrid}). Second, we confirm the effectiveness of asynchronous mode algorithms by comparing their
 performance with the synchronous mode. More precisely, we had implemented a program for solving large non-symmetric
 linear system of equations by numerical method GMRES (Generalized Minimal Residual) []. We show, that with minor
-modifications of the initial MPI code, the SimGrid toolkit allows us to perform a test campain of a real AIAC
+modifications of the initial MPI code, the SimGrid toolkit allows us to perform a test campaign of a real AIAC
 application on different computing architectures. The simulated results we obtained are in line with real results
 exposed in ??. SimGrid had allowed us to launch the application from a modest computing infrastructure by simulating
 different distributed architectures composed by clusters nodes interconnected by variable speed networks. It has been
@@ -152,7 +152,7 @@ performance, but also a time saving of up to \np[\%]{40} in asynchronous mode.
 
 This article is structured as follows: after this introduction, the next  section will give a brief description of
 iterative asynchronous model.  Then, the simulation framework SimGrid is presented with the settings to create various
-distributed architectures. The algorithm of  the multi-splitting method used by GMRES written with MPI primitives and
+distributed architectures. The algorithm of  the multisplitting method used by GMRES written with MPI primitives and
 its adaptation to SimGrid with SMPI (Simulated MPI) is detailed in the next section. At last, the experiments results
 carried out will be presented before some concluding remarks and future works.
  
@@ -160,17 +160,17 @@ carried out will be presented before some concluding remarks and future works.
 
 As exposed in the introduction, parallel iterative methods are now widely used in many scientific domains. They can be
 classified in three main classes depending on how iterations and communications are managed (for more details readers
-can refer to \cite{bcvc02:ip}). In the \textit{Synchronous Iterations - Synchronous Communications (SISC)} model data
+can refer to \cite{bcvc06:ij}). In the \textit{Synchronous Iterations~-- Synchronous Communications (SISC)} model data
 are exchanged at the end of each iteration. All the processors must begin the same iteration at the same time and
-important idle times on processors are generated. The \textit{Synchronous Iterations - Asynchronous Communications
+important idle times on processors are generated. The \textit{Synchronous Iterations~-- Asynchronous Communications
 (SIAC)} model can be compared to the previous one except that data required on another processor are sent asynchronously
 i.e.  without stopping current computations. This technique allows to partially overlap communications by computations
 but unfortunately, the overlapping is only partial and important idle times remain.  It is clear that, in a grid
 computing context, where the number of computational nodes is large, heterogeneous and widely distributed, the idle
 times generated by synchronizations are very penalizing. One way to overcome this problem is to use the
-\textit{Asynchronous Iterations - Asynchronous   Communications (AIAC)} model. Here, local computations do not need to
+\textit{Asynchronous Iterations~-- Asynchronous Communications (AIAC)} model. Here, local computations do not need to
 wait for required data. Processors can then perform their iterations with the data present at that time. Figure
-\ref{fig:aiac} illustrates this model where the grey blocks represent the computation phases, the white spaces the idle
+\ref{fig:aiac} illustrates this model where the gray blocks represent the computation phases, the white spaces the idle
 times and the arrows the communications. With this algorithmic model, the number of iterations required before the
 convergence is generally greater than for the two former classes. But, and as detailed in \cite{bcvc06:ij}, AIAC
 algorithms can significantly reduce overall execution times by suppressing idle times due to synchronizations especially
@@ -179,7 +179,7 @@ in a grid computing context.
 \begin{figure}[!t]
   \centering
     \includegraphics[width=8cm]{AIAC.pdf}
-  \caption{The Asynchronous Iterations - Asynchronous Communications model } 
+  \caption{The Asynchronous Iterations~-- Asynchronous Communications model}
   \label{fig:aiac}
 \end{figure}
 
@@ -193,7 +193,7 @@ simulation tools to explore various platform scenarios at will and to run enormo
 very promising. Several works...
 
 In the context of AIAC algorithms, the use of simulation tools is even more relevant. Indeed, this class of applications
-is very sensible to the execution environment context. For instance, variations in the network bandwith (intra and
+is very sensible to the execution environment context. For instance, variations in the network bandwidth (intra and
 inter-clusters), in the number and the power of nodes, in the number of clusters... can lead to very different number of
 iterations and so to very different execution times.
 
@@ -203,10 +203,10 @@ iterations and so to very different execution times.
 \section{SimGrid}
 
 SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} is a simulation
-framework to sudy the behavior of large-scale distributed systems.  As its name
+framework to study the behavior of large-scale distributed systems.  As its name
 says, it emanates from the grid computing community, but is nowadays used to
 study grids, clouds, HPC or peer-to-peer systems.  The early versions of SimGrid
-date from 1999, but it's still actively developped and distributed as an open
+date from 1999, but it's still actively developed and distributed as an open
 source software.  Today, it's one of the major generic tools in the field of
 simulation for large-scale distributed systems.
 
@@ -233,7 +233,7 @@ with little or no modifications.  SMPI implements about \np[\%]{80} of the MPI
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}
 %Décrire le problème (algo) traité ainsi que le processus d'adaptation à 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. In this case, we apply a row-by-row splitting without overlapping  
+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  
 \[
 \left(\begin{array}{ccc}
 A_{11} & \cdots & A_{1L} \\
@@ -320,7 +320,20 @@ where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the tole
 
 \LZK{Description du processus d'adaptation de l'algo multisplitting à SimGrid}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
+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 the six neighbors of each point in a submatrix 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. 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.
+As mentioned, upon this adaptation, the algorithm is executed as in the real life in the simulated environment after the following minor changes. First, all declared 
+global variables have been moved to local variables for each subroutine. In fact, global variables generate side effects arising from the concurrent access of 
+shared memory used by threads simulating each computing units in the SimGrid architecture. Second, the alignment of certain types of variables such as ``long int'' had
+also to be reviewed. Finally, some compilation errors on MPI\_Waitall and MPI\_Finalize primitives have been fixed with the latest version of SimGrid.
+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 tested in synchronous mode with a simulated platform starting from a modest 2 or 3 clusters grid to a larger configuration like simulating 
+Grid5000 with more than 1500 hosts with 5000 cores~\cite{bolze2006grid}. Once the code debugging and adaptation were complete, the next section shows our methodology and experimental 
+results.
 
 
 
@@ -507,7 +520,7 @@ the results have given a speedup less than 1, showing the effectiveness of the
 asynchronous performance compared to the synchronous mode.
 
 In the case of a two clusters configuration, Table~\ref{tab.cluster.2x50} shows
-that with a deterioration of inter cluster network set with \np[Mbits/s]{5} of
+that with a deterioration of inter cluster network set with \np[Mbit/s]{5} of
 bandwidth, a latency in order of a hundredth of a millisecond and a system power
 of one GFlops, an efficiency of about \np[\%]{40} in asynchronous mode is
 obtained for a matrix size of 62 elements. It is noticed that the result remains
@@ -516,7 +529,7 @@ increasing the problem size up to $100$ elements, it was necessary to increase t
 CPU power of \np[\%]{50} to \np[GFlops]{1.5} for a convergence of the algorithm
 with the same order of asynchronous mode efficiency.  Maintaining such a system
 power but this time, increasing network throughput inter cluster up to
-\np[Mbits/s]{50}, the result of efficiency of about \np[\%]{40} is obtained with
+\np[Mbit/s]{50}, the result of efficiency of about \np[\%]{40} is obtained with
 high external precision of \np{E-11} for a matrix size from $110$ to $150$ side
 elements.
 
@@ -525,13 +538,13 @@ Table~\ref{tab.cluster.3x33} shows that it was difficult to have a combination
 which gives an efficiency of asynchronous below \np[\%]{80}. Indeed, for a
 matrix size of $62$ elements, equality between the performance of the two modes
 (synchronous and asynchronous) is achieved with an inter cluster of
-\np[Mbits/s]{10} and a latency of \np[ms]{E-1}. To challenge an efficiency by
+\np[Mbit/s]{10} and a latency of \np[ms]{E-1}. To challenge an efficiency by
 \np[\%]{78} with a matrix size of $100$ points, it was necessary to degrade the
-inter cluster network bandwidth from 5 to 2 Mbit/s.
+inter cluster network bandwidth from 5 to \np[Mbit/s]{2}.
 
 A last attempt was made for a configuration of three clusters but more powerful
 with 200 nodes in total. The convergence with a speedup of \np[\%]{90} was
-obtained with a bandwidth of \np[Mbits/s]{1} as shown in
+obtained with a bandwidth of \np[Mbit/s]{1} as shown in
 Table~\ref{tab.cluster.3x67}.
 
 \section{Conclusion}
@@ -541,17 +554,15 @@ 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: 
 
-\newcounter{numberedCntD}
 \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 raisonnable time and 
+\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.
-\setcounter{numberedCntD}{\theenumi}
 \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
@@ -566,8 +577,8 @@ mode in a grid architecture.
 
 \section*{Acknowledgment}
 
-
-The authors would like to thank\dots{}
+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{}}
 
 
 % trigger a \newpage just before the given reference
@@ -585,3 +596,10 @@ The authors would like to thank\dots{}
 %%% fill-column: 80
 %%% ispell-local-dictionary: "american"
 %%% End:
+
+% LocalWords:  Ramamonjisoa Laiymani Arnaud Giersch Ziane Khodja Raphaël Femto
+% LocalWords:  Université Franche Comté IUT Montbéliard Maréchal Juin Inria Sud
+% LocalWords:  Ouest Vieille Talence cedex scalability experimentations HPC MPI
+% LocalWords:  Parallelization AIAC GMRES multi SMPI SISC SIAC SimDAG DAGs Lua
+% LocalWords:  Fortran GFlops priori Mbit de du fcomte multisplitting scalable
+% LocalWords:  SimGrid Belfort parallelize Labex ANR LABX IEEEabrv hpccBib