v7

[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 530ddb7a37ed6273519b23c8cba42a8a80f80743..6a39362badcb21cccadbc9380115562754ad6eed 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -82,8 +82,8 @@ what parameters  could influence or not  the behaviors of an  algorithm. In this
 paper, we show  that it is interesting to use SimGrid  to simulate the behaviors
 of asynchronous  iterative algorithms. For that,  we compare the  behaviour of a
 synchronous  GMRES  algorithm  with  an  asynchronous  multisplitting  one  with
 paper, we show  that it is interesting to use SimGrid  to simulate the behaviors
 of asynchronous  iterative algorithms. For that,  we compare the  behaviour of a
 synchronous  GMRES  algorithm  with  an  asynchronous  multisplitting  one  with

-simulations  in  which we  choose  some parameters.   Both  codes  are real  MPI
-codes. Simulations allow us to see when the multisplitting algorithm can be more
+simulations  which let us easily choose  some parameters.   Both  codes  are real  MPI
+codes and simulations allow us to see when the asynchronous multisplitting algorithm can be more

 efficient than the GMRES one to solve a 3D Poisson problem.
 
 
 efficient than the GMRES one to solve a 3D Poisson problem.
 
 


@@ -103,7 +103,7 @@ suggests, these algorithms solve a given problem by successive iterations ($X_{n
 $X_{0}$ 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}.
 
 $X_{0}$ 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 involve the division of the problem
+Parallelization of such algorithms generally involves 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
 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


@@ -228,13 +228,13 @@ In the context of asynchronous algorithms, the number of iterations to reach the
 convergence depends on  the delay of messages. With  synchronous iterations, the
 number of  iterations is exactly  the same than  in the sequential mode  (if the
 parallelization process does  not change the algorithm). So  the difficulty with
 convergence depends on  the delay of messages. With  synchronous iterations, the
 number of  iterations is exactly  the same than  in the sequential mode  (if the
 parallelization process does  not change the algorithm). So  the difficulty with

-asynchronous iteratie algorithms comes from the fact it is necessary to run the algorithm
+asynchronous iterative algorithms comes from the fact it is necessary to run the algorithm

 with real data. In fact, from an execution to another the order of messages will
 change and the  number of iterations to reach the  convergence will also change.
 According  to all  the parameters  of the  platform (number  of nodes,  power of
 with real data. In fact, from an execution to another the order of messages will
 change and the  number of iterations to reach the  convergence will also change.
 According  to all  the parameters  of the  platform (number  of nodes,  power of

-nodes,  inter  and  intra clusrters  bandwith  and  latency,  ....) and  of  the
-algorithm  (number   of  splitting  with  the   multisplitting  algorithm),  the
-multisplitting code  will obtain the solution  more or less  quickly. Or course,
+nodes,  inter  and  intra clusrters  bandwith  and  latency, etc.) and  of  the
+algorithm  (number   of  splittings  with  the   multisplitting  algorithm),  the
+multisplitting code  will obtain the solution  more or less  quickly. Of course,

 the GMRES method also depends of the same parameters. As it is difficult to have
 access to  many clusters,  grids or supercomputers  with many  different network
 parameters,  it  is  interesting  to  be  able  to  simulate  the  behaviors  of
 the GMRES method also depends of the same parameters. As it is difficult to have
 access to  many clusters,  grids or supercomputers  with many  different network
 parameters,  it  is  interesting  to  be  able  to  simulate  the  behaviors  of


@@ -251,8 +251,8 @@ 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
 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

-date from 1999, but it's still actively developed and distributed as an open
-source software.  Today, it's one of the major generic tools in the field of
+date from 1999, but it is still actively developed and distributed as an open
+source software.  Today, it is one of the major generic tools in the field of

 simulation for large-scale distributed systems.
 
 SimGrid provides several programming interfaces: MSG to simulate Concurrent
 simulation for large-scale distributed systems.
 
 SimGrid provides several programming interfaces: MSG to simulate Concurrent


@@ -384,7 +384,7 @@ exchanged by message passing using MPI non-blocking communication routines.
 \begin{figure}[!t]
 \centering
   \includegraphics[width=60mm,keepaspectratio]{clustering}
 \begin{figure}[!t]
 \centering
   \includegraphics[width=60mm,keepaspectratio]{clustering}

-\caption{Example of three clusters of processors interconnected by a virtual unidirectional ring network.}
+\caption{Example of three distant clusters of processors.}

 \label{fig:4.1}
 \end{figure}
 
 \label{fig:4.1}
 \end{figure}
 


@@ -395,9 +395,9 @@ processor is designated (for example the processor with rank 1) and masters of
 all clusters are interconnected by a virtual unidirectional ring network (see
 Figure~\ref{fig:4.1}). During the resolution, a Boolean token circulates around
 the virtual ring from a master processor to another until the global convergence
 all clusters are interconnected by a virtual unidirectional ring network (see
 Figure~\ref{fig:4.1}). During the resolution, a Boolean token circulates around
 the virtual ring from a master processor to another until the global convergence

-is achieved. So starting from the cluster with rank 1, each master processor $i$
+is achieved. So starting from the cluster with rank 1, each master processor $\ell$

 sets the token to \textit{True} if the local convergence is achieved or to
 sets the token to \textit{True} if the local convergence is achieved or to

-\textit{False} otherwise, and sends it to master processor $i+1$. Finally, the
+\textit{False} otherwise, and sends it to master processor $\ell+1$. Finally, the

 global convergence is detected when the master of cluster 1 receives from the
 master of cluster $L$ a token set to \textit{True}. In this case, the master of
 cluster 1 broadcasts a stop message to masters of other clusters. In this work,
 global convergence is detected when the master of cluster 1 receives from the
 master of cluster $L$ a token set to \textit{True}. In this case, the master of
 cluster 1 broadcasts a stop message to masters of other clusters. In this work,


@@ -422,7 +422,7 @@ u =0 \text{~on~} \Gamma =\partial\Omega
 \right.
 \label{eq:02}
 \end{equation}
 \right.
 \label{eq:02}
 \end{equation}

-where $\nabla^2$ is the Laplace operator, $f$ and $u$ are real-valued functions, and $\Omega=[0,1]^3$. The spatial discretization with a finite difference scheme reduces problem~(\ref{eq:02}) to a system of sparse linear equations. Our multisplitting method solves the 3D Poisson problem using a seven point stencil whose the general expression could be written as
+where $\nabla^2$ is the Laplace operator, $f$ and $u$ are real-valued functions, and $\Omega=[0,1]^3$. The spatial discretization with a finite differences scheme reduces problem~(\ref{eq:02}) to a system of sparse linear equations. Our multisplitting method solves the 3D Poisson problem using a seven point stencil whose the general expression could be written as

 \begin{equation}
 \begin{array}{l}
 u(x-1,y,z) + u(x,y-1,z) + u(x,y,z-1)\\+u(x+1,y,z)+u(x,y+1,z)+u(x,y,z+1) \\ -6u(x,y,z)=h^2f(x,y,z),
 \begin{equation}
 \begin{array}{l}
 u(x-1,y,z) + u(x,y-1,z) + u(x,y,z-1)\\+u(x+1,y,z)+u(x,y+1,z)+u(x,y,z+1) \\ -6u(x,y,z)=h^2f(x,y,z),


@@ -476,15 +476,14 @@ study that the results depend on the following parameters:
 \item Hosts processors power (GFlops) can also influence on the results.
 \item Finally, when submitting job batches for execution, the arguments values
   passed to the program like the maximum number of iterations or the precision are critical. They allow us to ensure not only the convergence of the
 \item Hosts processors power (GFlops) can also influence on the results.
 \item Finally, when submitting job batches for execution, the arguments values
   passed to the program like the maximum number of iterations or the precision are critical. They allow us to ensure not only the convergence of the

-  algorithm but also to get the main objective in getting an execution time in asynchronous communication less than in
-  synchronous mode (i.e. GMRES). 
+  algorithm but also to get the main objective in getting an execution time with the asynchronous multisplitting  less than with synchronous GMRES. 

   \end{itemize}
 
 The ratio between the simulated execution time of synchronous GMRES algorithm
 compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
 our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1.
 A priori, obtaining a relative gain greater than 1 would be difficult in a local
   \end{itemize}
 
 The ratio between the simulated execution time of synchronous GMRES algorithm
 compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
 our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1.
 A priori, obtaining a relative gain greater than 1 would be difficult in a local

-area network configuration where the synchronous mode will take advantage on the
+area network configuration where the synchronous GMRES method will take advantage on the

 rapid exchange of information on such high-speed links. Thus, the methodology
 adopted was to launch the application on a clustered network. In this
 configuration, degrading the inter-cluster network performance will penalize the
 rapid exchange of information on such high-speed links. Thus, the methodology
 adopted was to launch the application on a clustered network. In this
 configuration, degrading the inter-cluster network performance will penalize the


@@ -509,7 +508,8 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
 
 \begin{table}[!t]
   \centering
 
 \begin{table}[!t]
   \centering

-  \caption{2 clusters, each with 50 nodes}
+  \caption{Relative gain  of the multisplitting algorithm compared  to GMRES for
+    different configurations with 2 clusters, each one composed of 50 nodes.}

   \label{tab.cluster.2x50}
 
   \begin{mytable}{5}
   \label{tab.cluster.2x50}
 
   \begin{mytable}{5}


@@ -518,7 +518,7 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
     & 5         & 5         & 5         & 5         & 5         \\
     \hline
     latency (ms)
     & 5         & 5         & 5         & 5         & 5         \\
     \hline
     latency (ms)

-    & 0.02      & 0.02      & 0.02      & 0.02      & 0.02      \\
+    & 20      &  20      & 20      & 20      & 20      \\

     \hline
     power (GFlops)
     & 1         & 1         & 1         & 1.5       & 1.5       \\
     \hline
     power (GFlops)
     & 1         & 1         & 1         & 1.5       & 1.5       \\


@@ -543,7 +543,7 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
     & 50        & 50        & 50        & 50        & 50 \\ %       & 10        & 10 \\
     \hline
     latency (ms)
     & 50        & 50        & 50        & 50        & 50 \\ %       & 10        & 10 \\
     \hline
     latency (ms)

-    & 0.02      & 0.02      & 0.02      & 0.02      & 0.02 \\ %      & 0.03      & 0.01 \\
+    & 20      & 20      & 20      & 20      & 20 \\ %      & 0.03      & 0.01 \\

     \hline
     Power (GFlops)
     & 1.5       & 1.5       & 1.5       & 1.5       & 1.5 \\ %      & 1         & 1.5 \\
     \hline
     Power (GFlops)
     & 1.5       & 1.5       & 1.5       & 1.5       & 1.5 \\ %      & 1         & 1.5 \\


@@ -561,13 +561,15 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
   \end{mytable}
 \end{table}
   
   \end{mytable}
 \end{table}
   

+\RC{Du coup la latence est toujours la même, pourquoi la mettre dans la table?}
+

 %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
 %clusters. In the same way as above, a judicious choice of key parameters has
 %permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the
 %relative gains greater than 1 with a matrix size from 62 to 100 elements.
 
 %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
 %clusters. In the same way as above, a judicious choice of key parameters has
 %permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the
 %relative gains greater than 1 with a matrix size from 62 to 100 elements.
 

-\CER{En accord avec RC, on a pour le moment enlevé les tableaux 2 et 3 sachant que les résultats obtenus sont limites. De même, on a enlevé aussi les deux dernières colonnes du tableau I en attendant une meilleure performance et une meilleure precision}
+%\CER{En accord avec RC, on a pour le moment enlevé les tableaux 2 et 3 sachant que les résultats obtenus sont limites. De même, on a enlevé aussi les deux dernières colonnes du tableau I en attendant une meilleure performance et une meilleure precision}

 %\begin{table}[!t]
 %  \centering
 %  \caption{3 clusters, each with 33 nodes}
 %\begin{table}[!t]
 %  \centering
 %  \caption{3 clusters, each with 33 nodes}


@@ -634,8 +636,8 @@ Note that the program was run with the following parameters:
   \begin{itemize}
   \item 2 clusters of 50 hosts each;
   \item Processor unit power: \np[GFlops]{1} or \np[GFlops]{1.5};
   \begin{itemize}
   \item 2 clusters of 50 hosts each;
   \item Processor unit power: \np[GFlops]{1} or \np[GFlops]{1.5};

-  \item Intra-cluster network bandwidth: \np[Gbit/s]{1.25} and latency: \np[$\mu$s]{0.05};
-  \item Inter-cluster network bandwidth: \np[Mbit/s]{5} or \np[Mbit/s]{50} and latency: \np[$\mu$s]{20};
+  \item Intra-cluster network bandwidth: \np[Gbit/s]{1.25} and latency: \np[$\mu$s]{50};
+  \item Inter-cluster network bandwidth: \np[Mbit/s]{5} or \np[Mbit/s]{50} and latency: \np[ms]{20};

   \end{itemize}
 \end{itemize}
 
   \end{itemize}
 \end{itemize}
 


@@ -657,10 +659,10 @@ Note that the program was run with the following parameters:
 
 After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
 the results have given a relative gain more than 2.5, showing the effectiveness of the
 
 After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
 the results have given a relative gain more than 2.5, showing the effectiveness of the

-asynchronous performance compared to the synchronous mode.
+asynchronous multisplitting  compared to GMRES with two distant clusters.

 
 With these settings, Table~\ref{tab.cluster.2x50} shows
 
 With these settings, Table~\ref{tab.cluster.2x50} shows

-that after a deterioration of inter cluster network with a bandwidth of \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
+that after setting the bandwidth of the  inter cluster network to  \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power

 of one GFlops, an efficiency of about \np[\%]{40} is
 obtained in asynchronous mode for a matrix size of 62 elements. It is noticed that the result remains
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By
 of one GFlops, an efficiency of about \np[\%]{40} is
 obtained in asynchronous mode for a matrix size of 62 elements. It is noticed that the result remains
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By


@@ -690,39 +692,35 @@ elements.
 %\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??}
 %\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau INTER cluster.}
 \section{Conclusion}
 %\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??}
 %\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau INTER cluster.}
 \section{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. 
-Our work has demonstrated that using such a simulation tool allow us to 
-reach the following three objectives: 
+The simulation of the execution of parallel asynchronous iterative algorithms on large scale  clusters has been presented. 
+In this work, we show that SIMGRID is an efficient simulation tool that allows us to 
+reach the following two objectives: 

 
 \begin{enumerate}
 
 \begin{enumerate}

-\item To have a flexible configurable execution platform resolving the 
-hard exercise to access to very limited but so solicited physical 
-resources;
-\item to ensure the algorithm convergence with a reasonable time and
-iteration number ;
-\item and finally and more importantly, to find the correct combination 
-of the cluster and network specifications permitting to save time in 
-executing the algorithm in asynchronous mode.
+\item  To have  a flexible  configurable execution  platform that  allows  us to
+  simulate algorithms for  which execution of all parts of
+  the  code is  necessary. Using  simulations before  real executions  is  a nice
+  solution to detect potential scalability problems.
+
+\item To test the combination of the cluster and network specifications permitting to execute an asynchronous algorithm faster than a synchronous one.

 \end{enumerate}
 \end{enumerate}

-Our results have shown that in certain conditions, asynchronous mode is 
-speeder up to \np[\%]{40} than executing the algorithm in synchronous mode
+Our results have shown that with two distant clusters, the asynchronous multisplitting is faster to \np[\%]{40} compared to the synchronous GMRES method

 which is not negligible for solving complex practical problems with more 
 and more increasing size.
 
 which is not negligible for solving complex practical problems with more 
 and more increasing size.
 

- Several studies have already addressed the performance execution time of 
+Several studies have already addressed the performance execution time of 

 this class of algorithm. The work presented in this paper has 
 demonstrated an original solution to optimize the use of a simulation 
 tool to run efficiently an iterative parallel algorithm in asynchronous 
 mode in a grid architecture. 
 
 this class of algorithm. The work presented in this paper has 
 demonstrated an original solution to optimize the use of a simulation 
 tool to run efficiently an iterative parallel algorithm in asynchronous 
 mode in a grid architecture. 
 

-\LZK{Perspectives???}
+In future works, we plan to extend our experimentations to larger scale platforms by increasing the number of computing cores and the number of clusters. 
+We will also have to increase the size of the input problem which will require the use of a more powerful simulation platform. At last, we expect to compare our simulation results to real execution results on real architectures in order to experimentally validate our study.

 
 \section*{Acknowledgment}
 
 This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
 
 \section*{Acknowledgment}
 
 This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).

-\todo[inline]{The authors would like to thank\dots{}}
+%\todo[inline]{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
 
 % trigger a \newpage just before the given reference
 % number - used to balance the columns on the last page