\usepackage[utf8]{inputenc}
\usepackage{amsfonts,amssymb}
\usepackage{amsmath}
-\usepackage{algorithm}
+%\usepackage{algorithm}
\usepackage{algpseudocode}
%\usepackage{amsthm}
\usepackage{graphicx}
\usepackage[textsize=footnotesize]{todonotes}
\newcommand{\AG}[2][inline]{%
\todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}
-\newcommand{\RC}[2][inline]{%
- \todo[color=red!10,#1]{\sffamily\textbf{RC:} #2}\xspace}
+\newcommand{\DL}[2][inline]{%
+ \todo[color=yellow!50,#1]{\sffamily\textbf{DL:} #2}\xspace}
\newcommand{\LZK}[2][inline]{%
\todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
+\newcommand{\RC}[2][inline]{%
+ \todo[color=red!10,#1]{\sffamily\textbf{RC:} #2}\xspace}
\algnewcommand\algorithmicinput{\textbf{Input:}}
\algnewcommand\Input{\item[\algorithmicinput]}
\RC{Ordre des autheurs pas définitif.}
\begin{abstract}
-ABSTRACT
-
In recent years, the scalability of large-scale implementation in a
distributed environment of algorithms becoming more and more complex has
always been hampered by the limits of physical computing resources
during the execution. Two important factors determine the success of the
experimentation: the convergence of the iterative algorithm on a large
scale and the execution time reduction in asynchronous mode. Once again,
-from the current work, a simulated environment like Simgrid provides
+from the current work, a simulated environment like SimGrid provides
accurate results which are difficult or even impossible to obtain in a
physical platform by exploiting the flexibility of the simulator on the
computing units clusters and the network structure design. Our
simulated large scale growing environment and with larger problem size.
% no keywords for IEEE conferences
-% Keywords: Algorithm distributed iterative asynchronous simulation simgrid
+% Keywords: Algorithm distributed iterative asynchronous simulation SimGrid
\end{abstract}
\section{Introduction}
-Parallel computing and high performance computing (HPC) are becoming
-more and more imperative for solving various problems raised by
-researchers on various scientific disciplines but also by industrial in
-the field. Indeed, the 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\dots{}) but
-also a non-negligible CPU execution time. We consider in this paper a
-class of highly efficient parallel algorithms called iterative executed
-in a distributed environment. As their name suggests, these algorithm
-solves a given problem that might be NP- complete complex 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. Generally, to reduce the complexity and the
-execution time, the problem is divided into several \emph{pieces} that will
-be solved in parallel on multiple processing units. The latter will
-communicate each intermediate results before a new iteration starts
-until the approximate solution is reached. These distributed parallel
-computations can be performed either in \emph{synchronous} communication 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. Despite the
-effectiveness of iterative approach, a major drawback of the method is
-the requirement of huge resources in terms of computing capacity,
-storage and high speed communication network. Indeed, limited physical
-resources are blocking factors for large-scale deployment of parallel
-algorithms.
-
-In recent years, the use of a simulation environment to execute parallel
-iterative algorithms found some interests in reducing the highly cost of
-access to computing resources: (1) for the applications development life
-cycle and in code debugging (2) and in production to get results in a
-reasonable execution time with a simulated infrastructure not accessible
-with physical resources. Indeed, the launch of distributed iterative
-asynchronous algorithms to solve a given problem on a large-scale
-simulated environment challenges to find optimal configurations giving
-the best results with a lowest residual error and in the best of
-execution time. According our knowledge, no testing of large-scale
-simulation of the class of algorithm solving to achieve real results has
-been undertaken to date. We had in the scope of this work implemented a
-program for solving large non-symmetric linear system of equations by
-numerical method GMRES (Generalized Minimal Residual) in the simulation
-environment SimGrid. The simulated platform 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. In addition, it has been
-permitted to show the effectiveness of asynchronous mode algorithm by
-comparing its performance with the synchronous mode time. With selected
-parameters on the network platforms (bandwidth, latency of inter cluster
-network) and on the clusters architecture (number, capacity calculation
-power) in the simulated environment, the experimental results have
-demonstrated not only the algorithm convergence within a reasonable time
-compared with the physical environment performance, but also a time
+Parallel computing and high performance computing (HPC) are becoming more and more imperative for solving various
+problems raised by researchers on various scientific disciplines but also by industrial in the field. Indeed, the
+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
+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{}.
+
+Parallelization of such algorithms generally involved the division of the problem into several \emph{pieces} that will
+be solved in parallel on multiple processing units. The latter will communicate each intermediate results before a new
+iteration starts until the approximate solution is reached. These parallel computations can be performed
+either in \emph{synchronous} communication 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.
+
+% DL : reprendre correction ici
+Despite the effectiveness of iterative approach, a major drawback of the method is the requirement of huge
+resources in terms of computing capacity, storage and high speed communication network. Indeed, limited physical
+resources are blocking factors for large-scale deployment of parallel algorithms.
+
+In recent years, the use of a simulation environment to execute parallel iterative algorithms found some interests in
+reducing the highly cost of access to computing resources: (1) for the applications development life cycle and in code
+debugging (2) and in production to get results in a reasonable execution time with a simulated infrastructure not
+accessible with physical resources. Indeed, the launch of distributed iterative asynchronous algorithms to solve a
+given problem on a large-scale simulated environment challenges to find optimal configurations giving the best results
+with a lowest residual error and in the best of execution time. According our knowledge, no testing of large-scale
+simulation of the class of algorithm solving to achieve real results has been undertaken to date. We had in the scope
+of this work implemented a program for solving large non-symmetric linear system of equations by numerical method
+GMRES (Generalized Minimal Residual) in the simulation environment SimGrid. The simulated platform 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. In addition, it has been permitted to show the
+effectiveness of asynchronous mode algorithm by comparing its performance with the synchronous mode time. With selected
+parameters on the network platforms (bandwidth, latency of inter cluster network) and on the clusters architecture
+(number, capacity calculation power) in the simulated environment, the experimental results have demonstrated not only
+the algorithm convergence within a reasonable time compared with the physical environment 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 will be presented with the
-settings to create various distributed architectures. The algorithm of
-the multi -splitting method used by GMRES written with MPI primitives
-and its adaptation to SimGrid with SMPI (Simulated MPI) will be in the
-next section. At last, the experiments results carried out will be
-presented before the conclusion which we will announce the opening of
-our future work after the results.
+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 will be presented with the settings to create
+various distributed architectures. The algorithm of the multi-splitting method used by GMRES written with MPI
+primitives and its adaptation to SimGrid with SMPI (Simulated MPI) will be in the next section. At last, the experiments
+results carried out will be presented before the conclusion which we will announce the opening of our future work after
+the results.
-\section{The asynchronous iteration model}
+\section{Motivations and scientific context}
+
+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
+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
+(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
+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
+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
+in a grid computing context.
+
+\begin{figure}[htbp]
+ \centering
+ \includegraphics[width=8cm]{AIAC.pdf}
+ \caption{The Asynchronous Iterations - Asynchronous Communications model }
+ \label{fig:aiac}
+\end{figure}
-Décrire le modèle asynchrone. Je m'en charge (DL)
-\section{SimGrid}
-
-Décrire SimGrid~\cite{casanova+legrand+quinson.2008.simgrid} (Arnaud)
+It is very challenging to develop efficient applications for large scale, heterogeneous and distributed platforms such
+as computing grids. Researchers and engineers have to develop techniques for maximizing application performance of these
+multi-cluster platforms, by redesigning the applications and/or by using novel algorithms that can account for the
+composite and heterogeneous nature of the platform. Unfortunately, the deployment of such applications on these very
+large scale systems is very costly, labor intensive and time consuming. In this context, it appears that the use of
+simulation tools to explore various platform scenarios at will and to run enormous numbers of experiments quickly can be
+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
+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.
+\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
+says, it emanates from the grid computing community, but is nowadays used to
+study grids, clouds, HPC or peer-to-peer systems.
+%- open source, developped since 1999, one of the major solution in the field
+%
+SimGrid provides several programming interfaces: MSG to simulate Concurrent
+Sequential Processes, SimDAG to simulate DAGs of (parallel) tasks, and SMPI to
+run real applications written in MPI~\cite{MPI}. Apart from the native C
+interface, SimGrid provides bindings for the C++, Java, Lua and Ruby programming
+languages. The SMPI interface supports applications written in C or Fortran,
+with little or no modifications.
+%- implements most of MPI-2 \cite{ref} standard [CHECK]
+
+%%% explain simulation
+%- simulated processes folded in one real process
+%- simulates interactions on the network, fluid model
+%- able to skip long-lasting computations
+%- traces + visu?
+
+%%% platforms
+%- describe resources and their interconnection, with their properties
+%- XML files
+
+%%% validation + refs
+
+\AG{Décrire SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} (Arnaud)}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Simulation of the multisplitting method}
\end{equation}
is solved independently by a cluster and communications are required to update the right-hand side sub-vector $Y_l$, such that the sub-vectors $X_m$ represent the data dependencies between the clusters. As each sub-system (\ref{eq:4.1}) is solved in parallel by a cluster of processors, our multisplitting method uses an iterative method as an inner solver which is easier to parallelize and more scalable than a direct method. In this work, we use the parallel algorithm of GMRES method~\cite{ref1} which is one of the most used iterative method by many researchers.
-\begin{algorithm}
-\caption{A multisplitting solver with GMRES method}
+\begin{figure}
+ %%% IEEE instructions forbid to use an algorithm environment here, use figure
+ %%% instead
\begin{algorithmic}[1]
\Input $A_l$ (sparse sub-matrix), $B_l$ (right-hand side sub-vector)
\Output $X_l$ (solution sub-vector)\vspace{0.2cm}
\State \Return $X_l^k$
\EndFunction
\end{algorithmic}
+\caption{A multisplitting solver with GMRES method}
\label{algo:01}
-\end{algorithm}
+\end{figure}
-Algorithm~\ref{algo:01} shows the main key points of the multisplitting method to solve a large sparse linear system. This algorithm is based on an outer-inner iteration method where the parallel synchronous GMRES method is used to solve the inner iteration. It is executed in parallel by each cluster of processors. For all $l,m\in\{1,\ldots,L\}$, the matrices and vectors with the subscript $l$ represent the local data for cluster $l$, while $\{A_{lm}\}_{m\neq l}$ are off-diagonal matrices of sparse matrix $A$ and $\{X_m\}_{m\neq l}$ contain vector elements of solution $x$ shared with neighboring clusters. At every outer iteration $k$, asynchronous communications are performed between processors of the local cluster and those of distant clusters (lines $6$ and $7$ in Algorithm~\ref{algo:01}). The shared vector elements of the solution $x$ are exchanged by message passing using MPI non-blocking communication routines.
+Algorithm on Figure~\ref{algo:01} shows the main key points of the
+multisplitting method to solve a large sparse linear system. This algorithm is
+based on an outer-inner iteration method where the parallel synchronous GMRES
+method is used to solve the inner iteration. It is executed in parallel by each
+cluster of processors. For all $l,m\in\{1,\ldots,L\}$, the matrices and vectors
+with the subscript $l$ represent the local data for cluster $l$, while
+$\{A_{lm}\}_{m\neq l}$ are off-diagonal matrices of sparse matrix $A$ and
+$\{X_m\}_{m\neq l}$ contain vector elements of solution $x$ shared with
+neighboring clusters. At every outer iteration $k$, asynchronous communications
+are performed between processors of the local cluster and those of distant
+clusters (lines $6$ and $7$ in Figure~\ref{algo:01}). The shared vector
+elements of the solution $x$ are exchanged by message passing using MPI
+non-blocking communication routines.
\begin{figure}
\centering
\section{Experimental results}
-When the ``real'' application runs in the simulation environment and produces
+When the \emph{real} application runs in the simulation environment and produces
the expected results, varying the input parameters and the program arguments
allows us to compare outputs from the code execution. We have noticed from this
study that the results depend on the following parameters: (1) at the network
network latency (lat). (2) Hosts power (GFlops) can also influence on the
results. And finally, (3) when submitting job batches for execution, the
arguments values passed to the program like the maximum number of iterations or
-the ``external'' precision are critical to ensure not only the convergence of the
+the \emph{external} precision are critical to ensure not only the convergence of the
algorithm but also to get the main objective of the experimentation of the
simulation in having an execution time in asynchronous less than in synchronous
-mode, in others words, in having a ``speedup'' less than 1 (Speedup = Execution
-time in synchronous mode / Execution time in asynchronous mode).
+mode, in others words, in having a \emph{speedup} less than 1
+({speedup}${}={}${execution time in synchronous mode}${}/{}${execution time in
+asynchronous mode}).
A priori, obtaining a speedup less than 1 would be difficult in a local area
network configuration where the synchronous mode will take advantage on the rapid
As a first step, the algorithm was run on a network consisting of two clusters
containing fifty hosts each, totaling one hundred hosts. Various combinations of
the above factors have providing the results shown in Table~\ref{tab.cluster.2x50} with a matrix size
-ranging from Nx = Ny = Nz = 62 to 171 elements or from $62^{3} = \np{238328}$ to
+ranging from $N_x = N_y = N_z = 62 \text{ to } 171$ elements or from $62^{3} = \np{238328}$ to
$171^{3} = \np{5211000}$ entries.
Then we have changed the network configuration using three clusters containing
\item Description of the cluster architecture;
\item Maximum number of internal and external iterations;
\item Internal and external precisions;
- \item Matrix size NX, NY and NZ;
- \item Matrix diagonal value = 6.0;
+ \item Matrix size $N_x$, $N_y$ and $N_z$;
+ \item Matrix diagonal value: \np{6.0};
\item Execution Mode: synchronous or asynchronous.
\end{itemize}
\centering
\caption{2 clusters X 50 nodes}
\label{tab.cluster.2x50}
- \AG{Les images manquent dans le dépôt Git. Si ce sont vraiment des tableaux, utiliser un format vectoriel (eps ou pdf), et surtout pas de jpeg!}
+ \AG{Ces tableaux (\ref{tab.cluster.2x50}, \ref{tab.cluster.3x33} et
+ \ref{tab.cluster.3x67}) sont affreux. Utiliser un format vectoriel (eps ou
+ pdf) ou, mieux, les réécrire en \LaTeX{}. Réécrire les légendes proprement
+ également (\texttt{\textbackslash{}times} au lieu de \texttt{X} par ex.)}
\includegraphics[width=209pt]{img1.jpg}
\end{table}
\centering
\caption{3 clusters X 33 nodes}
\label{tab.cluster.3x33}
- \AG{Le fichier manque.}
+ \AG{Refaire le tableau.}
\includegraphics[width=209pt]{img2.jpg}
\end{table}
\centering
\caption{3 clusters X 67 nodes}
\label{tab.cluster.3x67}
- \AG{Le fichier manque.}
+ \AG{Refaire le tableau.}
% \includegraphics[width=160pt]{img3.jpg}
\includegraphics[scale=0.5]{img3.jpg}
\end{table}
with a bandwidth of \np[Mbits/s]{1} as shown in Table~\ref{tab.cluster.3x67}.
\section{Conclusion}
-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.
% adjust value as needed - may need to be readjusted if
% the document is modified later
\bibliographystyle{IEEEtran}
-\bibliography{hpccBib}
+\bibliography{IEEEabrv,hpccBib}
\end{document}
