Typographical errors.

[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 9fcb5d8317d475ed18be189685ff02a72a84f4c5..2e791d7e35b2b126e4a090d06c28a67bd1522cd8 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -14,6 +14,14 @@
 % et l'affichage correct des URL (commande \url{http://example.com})
 %\usepackage{hyperref}
 
 % 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]}
 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}
 


@@ -36,7 +44,7 @@
     Femto-ST Institute - DISC Department\\
     Université de Franche-Comté\\
     Belfort\\
     Femto-ST Institute - DISC Department\\
     Université de Franche-Comté\\
     Belfort\\

-    Email: raphael.couturier@univ-fcomte.fr
+    Email: \email{raphael.couturier@univ-fcomte.fr}

   }
 }
 
   }
 }
 


@@ -54,13 +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 
 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 
 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 
 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 


@@ -90,8 +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 
 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 
 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 


@@ -99,18 +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 
 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 
 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. 
 
 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 
 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.
  
 presented before the conclusion which we will announce the opening of 
 our future work after the results.
  


@@ -223,8 +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
 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
 
 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


@@ -240,10 +248,10 @@ Note that the program was run with the following parameters:
 \paragraph*{SMPI parameters}
 
 \begin{itemize}
 \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,
        \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}
 
 
 \end{itemize}
 
 


@@ -253,7 +261,7 @@ lat latency , ... ).
        \item Description of the cluster architecture;
        \item Maximum number of internal and external iterations;
        \item Internal and external precisions;
        \item 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}
        \item Matrix diagonal value = 6.0;
        \item Execution Mode: synchronous or asynchronous.
 \end{itemize}


@@ -289,36 +297,36 @@ 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
 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
 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
 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
 
 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
 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
 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}
 
 \section*{Acknowledgment}
 
 
 
 \section{Conclusion}
 
 \section*{Acknowledgment}
 
 

-The authors would like to thank...
+The authors would like to thank\dots{}

 
 
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