From: Arnaud Giersch Date: Fri, 11 Apr 2014 15:04:21 +0000 (+0200) Subject: Misc. corrections. X-Git-Tag: hpcc2014_submission~116 X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/commitdiff_plain/923e1fe5e990dcc4a47997cc9cfe37cffda3159a?ds=sidebyside Misc. corrections. --- diff --git a/hpcc.tex b/hpcc.tex index 94e9ee7..02940f0 100644 --- a/hpcc.tex +++ b/hpcc.tex @@ -71,8 +71,6 @@ \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 @@ -87,7 +85,7 @@ balance and a compromise between computation and communication time 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 @@ -98,7 +96,7 @@ perspectives on experimentations for running the algorithm on a 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} @@ -109,11 +107,11 @@ 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 +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 iterative executed in a distributed environment. As their name suggests, these algorithm -solves a given problem that might be NP- complete complex by successive +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 @@ -163,7 +161,7 @@ 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 +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 @@ -264,7 +262,7 @@ where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the tole \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 @@ -272,11 +270,12 @@ level, we found that the most critical values are the bandwidth (bw) and the 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 @@ -289,7 +288,7 @@ 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 $62^{3} = \np{238328}$ 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 @@ -319,8 +318,8 @@ lat latency, \dots{}). \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} @@ -386,8 +385,6 @@ with 200 nodes in total. The convergence with a speedup of \np[\%]{90} was obtai 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.