X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/e9e06195c9dfa2fc247a414ba425d21a0d781c10..9db72b31bc5ae56df6c06f94f031aeb35876dd01:/hpcc.tex diff --git a/hpcc.tex b/hpcc.tex index e201e81..2e791d7 100644 --- a/hpcc.tex +++ b/hpcc.tex @@ -1,322 +1,4 @@ - -%% bare_conf.tex -%% V1.3 -%% 2007/01/11 -%% by Michael Shell -%% See: -%% http://www.michaelshell.org/ -%% for current contact information. -%% -%% This is a skeleton file demonstrating the use of IEEEtran.cls -%% (requires IEEEtran.cls version 1.7 or later) with an IEEE conference paper. -%% -%% Support sites: -%% http://www.michaelshell.org/tex/ieeetran/ -%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/ -%% and -%% http://www.ieee.org/ - -%%************************************************************************* -%% Legal Notice: -%% This code is offered as-is without any warranty either expressed or -%% implied; without even the implied warranty of MERCHANTABILITY or -%% FITNESS FOR A PARTICULAR PURPOSE! -%% User assumes all risk. -%% In no event shall IEEE or any contributor to this code be liable for -%% any damages or losses, including, but not limited to, incidental, -%% consequential, or any other damages, resulting from the use or misuse -%% of any information contained here. -%% -%% All comments are the opinions of their respective authors and are not -%% necessarily endorsed by the IEEE. -%% -%% This work is distributed under the LaTeX Project Public License (LPPL) -%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used, -%% distributed and modified. 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Version 1.3 (2005/06/28) and later -% (recommended due to many improvements over 1.2) of subfig.sty supports -% the caption=false option directly: -%\usepackage[caption=false,font=footnotesize]{subfig} -% -% The latest version and documentation can be obtained at: -% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/ -% The latest version and documentation of caption.sty can be obtained at: -% http://www.ctan.org/tex-archive/macros/latex/contrib/caption/ - - - - -% *** FLOAT PACKAGES *** -% -%\usepackage{fixltx2e} -% fixltx2e, the successor to the earlier fix2col.sty, was written by -% Frank Mittelbach and David Carlisle. This package corrects a few problems -% in the LaTeX2e kernel, the most notable of which is that in current -% LaTeX2e releases, the ordering of single and double column floats is not -% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a -% single column figure to be placed prior to an earlier double column -% figure. The latest version and documentation can be found at: -% http://www.ctan.org/tex-archive/macros/latex/base/ - - - -%\usepackage{stfloats} -% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e -% the ability to do double column floats at the bottom of the page as well -% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in -% LaTeX2e). It also provides a command: -%\fnbelowfloat -% to enable the placement of footnotes below bottom floats (the standard -% LaTeX2e kernel puts them above bottom floats). This is an invasive package -% which rewrites many portions of the LaTeX2e float routines. It may not work -% with other packages that modify the LaTeX2e float routines. The latest -% version and documentation can be obtained at: -% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/ -% Documentation is contained in the stfloats.sty comments as well as in the -% presfull.pdf file. Do not use the stfloats baselinefloat ability as IEEE -% does not allow \baselineskip to stretch. Authors submitting work to the -% IEEE should note that IEEE rarely uses double column equations and -% that authors should try to avoid such use. Do not be tempted to use the -% cuted.sty or midfloat.sty packages (also by Sigitas Tolusis) as IEEE does -% not format its papers in such ways. - - - - - -% *** PDF, URL AND HYPERLINK PACKAGES *** -% -%\usepackage{url} -% url.sty was written by Donald Arseneau. It provides better support for -% handling and breaking URLs. url.sty is already installed on most LaTeX -% systems. The latest version can be obtained at: -% http://www.ctan.org/tex-archive/macros/latex/contrib/misc/ -% Read the url.sty source comments for usage information. Basically, -% \url{my_url_here}. - -% *** Do not adjust lengths that control margins, column widths, etc. *** -% *** Do not use packages that alter fonts (such as pslatex). *** -% There should be no need to do such things with IEEEtran.cls V1.6 and later. -% (Unless specifically asked to do so by the journal or conference you plan -% to submit to, of course. ) - - \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} @@ -332,6 +14,14 @@ % et l'affichage correct des URL (commande \url{http://example.com}) %\usepackage{hyperref} +\usepackage{url} +\DeclareUrlCommand\email{\urlstyle{same}} + +\usepackage[autolanguage,np]{numprint} +\AtBeginDocument{% + \renewcommand*\npunitcommand[1]{\text{#1}} + \npthousandthpartsep{}} + \algnewcommand\algorithmicinput{\textbf{Input:}} \algnewcommand\Input{\item[\algorithmicinput]} @@ -339,69 +29,30 @@ \algnewcommand\Output{\item[\algorithmicoutput]} - - \begin{document} -% -% paper title -% can use linebreaks \\ within to get better formatting as desired -\title{Simulation of Asynchronous Iterative Numerical Algorithms Using SimGrid} +\title{Simulation of Asynchronous Iterative Numerical Algorithms Using SimGrid} -% author names and affiliations -% use a multiple column layout for up to three different -% affiliations -\author{\IEEEauthorblockN{Raphaël Couturier and Arnaud Giersch and David Laiymani and Charles Emile Ramamonjisoa} -\IEEEauthorblockA{Femto-ST Institute - DISC Department\\ -Université de Franche-Comté\\ -Belfort\\ -Email: raphael.couturier@univ-fcomte.fr} -%\and -%\IEEEauthorblockN{Arnaud Giersch} -%\IEEEauthorblockA{Twentieth Century Fox\\ -%Springfield, USA\\ -%Email: homer@thesimpsons.com} -%\and -%\IEEEauthorblockN{James Kirk\\ and Montgomery Scott} -%\IEEEauthorblockA{Starfleet Academy\\ -%San Francisco, California 96678-2391\\ -%Telephone: (800) 555--1212\\ -%Fax: (888) 555--1212 +\author{% + \IEEEauthorblockN{% + Raphaël Couturier, + Arnaud Giersch, + David Laiymani and + Charles Emile Ramamonjisoa + } + \IEEEauthorblockA{% + Femto-ST Institute - DISC Department\\ + Université de Franche-Comté\\ + Belfort\\ + Email: \email{raphael.couturier@univ-fcomte.fr} + } } - - -% make the title area \maketitle - \begin{abstract} -%\boldmath The abstract goes here. \end{abstract} -% IEEEtran.cls defaults to using nonbold math in the Abstract. -% This preserves the distinction between vectors and scalars. However, -% if the conference you are submitting to favors bold math in the abstract, -% then you can use LaTeX's standard command \boldmath at the very start -% of the abstract to achieve this. Many IEEE journals/conferences frown on -% math in the abstract anyway. - -% no keywords - - - - -% For peer review papers, you can put extra information on the cover -% page as needed: -% \ifCLASSOPTIONpeerreview -% \begin{center} \bfseries EDICS Category: 3-BBND \end{center} -% \fi -% -% For peerreview papers, this IEEEtran command inserts a page break and -% creates the second title. It will be ignored for other modes. -\IEEEpeerreviewmaketitle - - \section{Introduction} @@ -411,13 +62,13 @@ 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 +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 +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 "pieces" that will @@ -447,8 +98,8 @@ 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 +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 @@ -456,18 +107,18 @@ 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 +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 40 \% in asynchronous mode. +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 +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 (Simulation MPI ) will be in the -next section . At last, the experiments results carried out will be +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. @@ -580,8 +231,8 @@ clusters linked with long distance network like Internet. 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$^{3}$ = 238328 to -171$^{3}$ = 5,211,000 entries. +ranging from Nx = Ny = Nz = 62 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 respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the @@ -597,10 +248,10 @@ Note that the program was run with the following parameters: \paragraph*{SMPI parameters} \begin{itemize} - \item HOSTFILE : Hosts file description. + \item HOSTFILE: Hosts file description. \item PLATFORM: file description of the platform architecture : clusters (CPU power, -... ) , intra cluster network description, inter cluster network (bandwidth bw , -lat latency , ... ). +\dots{}), intra cluster network description, inter cluster network (bandwidth bw, +lat latency, \dots{}). \end{itemize} @@ -610,7 +261,7 @@ lat latency , ... ). \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 size NX, NY and NZ; \item Matrix diagonal value = 6.0; \item Execution Mode: synchronous or asynchronous. \end{itemize} @@ -646,168 +297,45 @@ 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 5 Mbits/s of bandwidth, a latency +deterioration of inter cluster network set with \np[Mbits/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 40\% in asynchronous mode is obtained for a matrix size of 62 -elements . It is noticed that the result remains stable even if we vary the -external precision from E -05 to E-09. By increasing the problem size up to 100 -elements, it was necessary to increase the CPU power of 50 \% to 1.5 GFlops for a +efficiency of about \np[\%]{40} in asynchronous mode is obtained for a matrix size of 62 +elements. It is noticed that the result remains stable even if we vary the +external precision from \np{E-5} to \np{E-9}. By increasing the problem size up to 100 +elements, it was necessary to increase the 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 50 Mbits /s, the result of efficiency of about 40\% is -obtained with high external precision of E-11 for a matrix size from 110 to 150 -side elements . +inter cluster up to \np[Mbits/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. For the 3 clusters architecture including a total of 100 hosts, Table~\ref{tab.cluster.3x33} shows that it was difficult to have a combination which gives an efficiency of -asynchronous below 80 \%. Indeed, for a matrix size of 62 elements, equality +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 10 Mbits/s and a latency of E- 01 ms. To -challenge an efficiency by 78\% with a matrix size of 100 points, it was +achieved with an inter cluster of \np[Mbits/s]{10} and a latency of \np{E-1} ms. 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. A last attempt was made for a configuration of three clusters but more power -with 200 nodes in total. The convergence with a speedup of 90 \% was obtained -with a bandwidth of 1 Mbits/s as shown in Table~\ref{tab.cluster.3x67}. +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 Table~\ref{tab.cluster.3x67}. \section{Conclusion} - -% An example of a floating figure using the graphicx package. -% Note that \label must occur AFTER (or within) \caption. -% For figures, \caption should occur after the \includegraphics. -% Note that IEEEtran v1.7 and later has special internal code that -% is designed to preserve the operation of \label within \caption -% even when the captionsoff option is in effect. However, because -% of issues like this, it may be the safest practice to put all your -% \label just after \caption rather than within \caption{}. -% -% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class -% option should be used if it is desired that the figures are to be -% displayed while in draft mode. -% -%\begin{figure}[!t] -%\centering -%\includegraphics[width=2.5in]{myfigure} -% where an .eps filename suffix will be assumed under latex, -% and a .pdf suffix will be assumed for pdflatex; or what has been declared -% via \DeclareGraphicsExtensions. -%\caption{Simulation Results} -%\label{fig_sim} -%\end{figure} - -% Note that IEEE typically puts floats only at the top, even when this -% results in a large percentage of a column being occupied by floats. - - -% An example of a double column floating figure using two subfigures. -% (The subfig.sty package must be loaded for this to work.) -% The subfigure \label commands are set within each subfloat command, the -% \label for the overall figure must come after \caption. -% \hfil must be used as a separator to get equal spacing. -% The subfigure.sty package works much the same way, except \subfigure is -% used instead of \subfloat. -% -%\begin{figure*}[!t] -%\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}% -%\label{fig_first_case}} -%\hfil -%\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}% -%\label{fig_second_case}}} -%\caption{Simulation results} -%\label{fig_sim} -%\end{figure*} -% -% Note that often IEEE papers with subfigures do not employ subfigure -% captions (using the optional argument to \subfloat), but instead will -% reference/describe all of them (a), (b), etc., within the main caption. - - -% An example of a floating table. Note that, for IEEE style tables, the -% \caption command should come BEFORE the table. Table text will default to -% \footnotesize as IEEE normally uses this smaller font for tables. -% The \label must come after \caption as always. -% -%\begin{table}[!t] -%% increase table row spacing, adjust to taste -%\renewcommand{\arraystretch}{1.3} -% if using array.sty, it might be a good idea to tweak the value of -% \extrarowheight as needed to properly center the text within the cells -%\caption{An Example of a Table} -%\label{table_example} -%\centering -%% Some packages, such as MDW tools, offer better commands for making tables -%% than the plain LaTeX2e tabular which is used here. -%\begin{tabular}{|c||c|} -%\hline -%One & Two\\ -%\hline -%Three & Four\\ -%\hline -%\end{tabular} -%\end{table} - - -% Note that IEEE does not put floats in the very first column - or typically -% anywhere on the first page for that matter. Also, in-text middle ("here") -% positioning is not used. Most IEEE journals/conferences use top floats -% exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places -% footnotes above bottom floats. This can be corrected via the \fnbelowfloat -% command of the stfloats package. - - - - - - - -% conference papers do not normally have an appendix - - -% use section* for acknowledgement \section*{Acknowledgment} -The authors would like to thank... - - - +The authors would like to thank\dots{} % trigger a \newpage just before the given reference % number - used to balance the columns on the last page % adjust value as needed - may need to be readjusted if % the document is modified later -%\IEEEtriggeratref{8} -% The "triggered" command can be changed if desired: -%\IEEEtriggercmd{\enlargethispage{-5in}} - -% references section - -% can use a bibliography generated by BibTeX as a .bbl file -% BibTeX documentation can be easily obtained at: -% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/ -% The IEEEtran BibTeX style support page is at: -% http://www.michaelshell.org/tex/ieeetran/bibtex/ \bibliographystyle{IEEEtran} -% argument is your BibTeX string definitions and bibliography database(s) \bibliography{hpccBib} -% -% manually copy in the resultant .bbl file -% set second argument of \begin to the number of references -% (used to reserve space for the reference number labels box) -%\begin{thebibliography}{1} -% -%\bibitem{IEEEhowto:kopka} -%H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus -% 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999. -% -%\end{thebibliography} - - - -% that's all folks \end{document} %%% Local Variables: