X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/f2d52a8e01117d631783d873860e90d32f2bf8d5..774b7cd45da63cb7d2c5b2b57a5f7cb775344a59:/hpcc.tex?ds=sidebyside

diff --git a/hpcc.tex b/hpcc.tex
index 497ed68..dd06eeb 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -106,15 +106,15 @@ increasing complexity of these requested  applications combined with a continuou
 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 \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
+suggests, these algorithms solve 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{BT89,Bahi07}. 
 
-Parallelization of such algorithms generally involved the division of the problem into several \emph{blocks} that will
+Parallelization of such algorithms generally involve 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
+\emph{synchronous} mode where a new iteration begins only when all nodes communications are completed,
+or in \emph{asynchronous} mode where processors can continue independently with few or no synchronization points. For
 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
@@ -143,9 +143,9 @@ performance with the synchronous mode. More precisely, we had implemented a prog
 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 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
-permitted to show  With selected parameters on the network platforms (bandwidth, latency of inter  cluster network) and
+exposed in ??\AG[]{??}. 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.
+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.
@@ -202,7 +202,7 @@ iterations and so to very different execution times.
 
 \section{SimGrid}
 
-SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} is a simulation
+SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid} is a simulation
 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
@@ -372,13 +372,20 @@ Table~\ref{tab.cluster.2x50} with a matrix size 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.
 
+% use the same column width for the following three tables
+\newlength{\mytablew}\settowidth{\mytablew}{\footnotesize\np{E-11}}
+\newenvironment{mytable}[1]{% #1: number of columns for data
+  \renewcommand{\arraystretch}{1.3}%
+  \begin{tabular}{|>{\bfseries}r%
+                  |*{#1}{>{\centering\arraybackslash}p{\mytablew}|}}}{%
+    \end{tabular}}
+
 \begin{table}[!t]
   \centering
   \caption{$2$ clusters, each with $50$ nodes}
   \label{tab.cluster.2x50}
-  \renewcommand{\arraystretch}{1.3}
 
-  \begin{tabular}{|>{\bfseries}r|*{12}{c|}}
+  \begin{mytable}{6}
     \hline
     bw
     & 5         & 5         & 5         & 5         & 5         & 50 \\
@@ -398,11 +405,11 @@ Table~\ref{tab.cluster.2x50} with a matrix size ranging from $N_x = N_y = N_z =
     speedup
     & 0.396     & 0.392     & 0.396     & 0.391     & 0.393     & 0.395 \\
     \hline
-  \end{tabular}
+  \end{mytable}
 
   \smallskip
 
-  \begin{tabular}{|>{\bfseries}r|*{12}{c|}}
+  \begin{mytable}{6}
     \hline
     bw
     & 50        & 50        & 50        & 50        & 10        & 10 \\
@@ -422,7 +429,7 @@ Table~\ref{tab.cluster.2x50} with a matrix size ranging from $N_x = N_y = N_z =
     speedup
     & 0.398     & 0.388     & 0.393     & 0.394     & 0.63      & 0.778 \\
     \hline
-  \end{tabular}
+  \end{mytable}
 \end{table}
   
 Then we have changed the network configuration using three clusters containing
@@ -435,9 +442,8 @@ speedups less than $1$ with a matrix size from $62$ to $100$ elements.
   \centering
   \caption{$3$ clusters, each with $33$ nodes}
   \label{tab.cluster.3x33}
-  \renewcommand{\arraystretch}{1.3}
 
-  \begin{tabular}{|>{\bfseries}r|*{6}{c|}}
+  \begin{mytable}{6}
     \hline
     bw
     & 10       & 5        & 4        & 3        & 2        & 6 \\
@@ -457,10 +463,9 @@ speedups less than $1$ with a matrix size from $62$ to $100$ elements.
     speedup
     & 0.997    & 0.99     & 0.93     & 0.84     & 0.78     & 0.99 \\
     \hline
-  \end{tabular}
+  \end{mytable}
 \end{table}
 
-
 In a final step, results of an execution attempt to scale up the three clustered
 configuration but increasing by two hundreds hosts has been recorded in
 Table~\ref{tab.cluster.3x67}.
@@ -469,9 +474,8 @@ Table~\ref{tab.cluster.3x67}.
   \centering
   \caption{3 clusters, each with 66 nodes}
   \label{tab.cluster.3x67}
-  \renewcommand{\arraystretch}{1.3}
 
-  \begin{tabular}{|>{\bfseries}r|c|}
+  \begin{mytable}{1}
     \hline
     bw         & 1 \\
     \hline
@@ -485,7 +489,7 @@ Table~\ref{tab.cluster.3x67}.
     \hline
     speedup    & 0.9 \\
     \hline
- \end{tabular}
+ \end{mytable}
 \end{table}
 
 Note that the program was run with the following parameters:
