X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/eee5d96ed771994c95b62ea44cf071ed66dde1a8..1bc416301f8ca538fdb365309936bfe6c53fe68a:/paper.tex?ds=sidebyside

diff --git a/paper.tex b/paper.tex
index a4d8085..bae87d3 100644
--- a/paper.tex
+++ b/paper.tex
@@ -90,7 +90,7 @@ analysis of simulated grid-enabled numerical iterative algorithms}
 
 %% Lilia Ziane Khodja: Department of Aerospace \& Mechanical Engineering\\ Non Linear Computational Mechanics\\ University of Liege\\ Liege, Belgium. Email: l.zianekhodja@ulg.ac.be
 
-\begin{abstract}   The behavior of multicore applications is always a challenge
+\begin{abstract}   The behavior of multi-core applications is always a challenge
 to predict, especially with a new architecture for which no experiment has been
 performed. With some applications, it is difficult, if not impossible, to build
 accurate performance models. That is why another solution is to use a simulation
@@ -101,7 +101,7 @@ applications.
 
 In this paper, we focus our attention on two parallel iterative algorithms based
 on the  Multisplitting algorithm  and we  compare them  to the  GMRES algorithm.
-These algorithms  are used to  solve libear  systems. Two different  variantsof
+These algorithms  are used to  solve libear  systems. Two different  variants of
 the Multisplitting are studied: one  using synchronoous  iterations and  another
 one  with asynchronous iterations. For each algorithm we have  tested different
 parameters to see their influence.  We strongly  recommend people  interested
@@ -119,8 +119,8 @@ their  applications  using  a simulation tool before.
 
 \maketitle
 
-\section{Introduction}  The use of multi-core architectures for solving large
-scientific problems seems to  become imperative  in  a  lot  of  cases.
+\section{Introduction}  The use of multi-core architectures to solve large
+scientific problems seems to  become imperative  in  many situations.
 Whatever the scale of these architectures (distributed clusters, computational
 grids, embedded multi-core,~\ldots) they  are generally  well adapted to execute
 complex parallel applications operating on a large amount of data.
@@ -131,8 +131,7 @@ are often very important. So, in this context it is difficult to optimize a
 given application for a given  architecture. In this way and in order to reduce
 the access cost to these computing resources it seems very interesting to use a
 simulation environment.  The advantages are numerous: development life cycle,
-code debugging, ability to obtain results quickly,~\ldots at the condition that
-the simulation results are in education with the real ones.
+code debugging, ability to obtain results quickly,~\ldots. In counterpart, the simulation results need to be consistent with the real ones.
 
 In this paper we focus on a class of highly efficient parallel algorithms called
 \emph{iterative algorithms}. The parallel scheme of iterative methods is quite
@@ -147,7 +146,7 @@ from its neighbors. We say that the iteration computation follows a synchronous
 scheme. In the asynchronous scheme a task can compute a new iteration without
 having to wait for the data dependencies coming from its neighbors. Both
 communication and computations are asynchronous inducing that there is no more
-idle times, due to synchronizations, between two iterations~\cite{bcvc06:ij}.
+idle time, due to synchronizations, between two iterations~\cite{bcvc06:ij}.
 This model presents some advantages and drawbacks that we detail in
 section~\ref{sec:asynchro} but even if the number of iterations required to
 converge is generally  greater  than for the synchronous  case, it appears that
@@ -155,15 +154,15 @@ the asynchronous  iterative scheme  can significantly  reduce  overall execution
 times by  suppressing idle  times due to  synchronizations~(see~\cite{bahi07}
 for more details).
 
-Nevertheless, in both cases (synchronous or asynchronous) it is very time
-consuming to find optimal configuration and deployment requirements  for a given
-application on a given multi-core architecture. Finding good resource
-allocations policies under varying CPU power, network speeds and  loads is very
-challenging and labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. This
-problematic is even more difficult for the asynchronous scheme  where variations
-of the parameters of the execution platform can lead to very different number of
-iterations required to converge and so to very different execution times. In
-this challenging context we think that the use of a simulation tool can greatly
+Nevertheless,  in both  cases  (synchronous  or asynchronous)  it  is very  time
+consuming to find optimal configuration  and deployment requirements for a given
+application  on   a  given   multi-core  architecture.  Finding   good  resource
+allocations policies under  varying CPU power, network speeds and  loads is very
+challenging and  labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. This
+problematic is  even more difficult  for the  asynchronous scheme where  a small
+parameter variation of the execution platform can lead to very different numbers
+of iterations to reach the converge and so to very different execution times. In
+this challenging context we think that the  use of a simulation tool can greatly
 leverage the possibility of testing various platform scenarios.
 
 The main contribution of this paper is to show that the use of a simulation tool
@@ -175,7 +174,7 @@ algorithm  with  the  GMRES   (Generalized   Minimal  Residual)
 solver~\cite{saad86} in synchronous mode. The obtained results on different
 simulated multi-core architectures confirm the real results previously obtained
 on non simulated architectures.  We also confirm  the efficiency  of the
-asynchronous  multisplitting algorithm  comparing to the synchronous  GMRES. In
+asynchronous  multisplitting algorithm  compared to the synchronous  GMRES. In
 this way and with a simple computing architecture (a laptop) SimGrid allows us
 to run a test campaign  of  a  real parallel iterative  applications on
 different simulated multi-core architectures.  To our knowledge, there is no
@@ -193,6 +192,27 @@ concluding remarks and perspectives.
 \section{The asynchronous iteration model}
 \label{sec:asynchro}
 
+Asynchronous iterative methods have been  studied for many years theoritecally and
+practically. Many methods have been considered and convergence results have been
+proved. These  methods can  be used  to solve, in  parallel, fixed  point problems
+(i.e. problems  for which  the solution is  $x^\star =f(x^\star)$.  In practice,
+asynchronous iterations  methods can be used  to solve, for example,  linear and
+non-linear systems of equations or optimization problems, interested readers are
+invited to read~\cite{BT89,bahi07}.
+
+Before  using  an  asynchronous  iterative   method,  the  convergence  must  be
+studied. Otherwise, the  application is not ensure to reach  the convergence. An
+algorithm that supports both the synchronous or the asynchronous iteration model
+requires very few modifications  to be able to be executed  in both variants. In
+practice, only  the communications and  convergence detection are  different. In
+the synchronous  mode, iterations are  synchronized whereas in  the asynchronous
+one, they are not.  It should be noticed that non blocking communications can be
+used in both  modes. Concerning the convergence  detection, synchronous variants
+can use  a global convergence procedure  which acts as a  global synchronization
+point. In the  asynchronous model, the convergence detection is  more tricky as
+it   must  not   synchronize  all   the  processors.   Interested  readers   can
+consult~\cite{myBCCV05c,bahi07,ccl09:ij}.
+
 \section{SimGrid}
  \label{sec:simgrid}
 
@@ -312,7 +332,7 @@ In addition, the following arguments are given to the programs at runtime:
 	\item Execution Mode: synchronous or asynchronous.
 \end{itemize}
 
-At last, note that the two solver algorithms have been executed with the Simgrid selector -cfg=smpi/running\_power which determine the computational power (here 19GFlops) of the simulator host machine.
+At last, note that the two solver algorithms have been executed with the Simgrid selector -cfg=smpi/running\_power which determines the computational power (here 19GFlops) of the simulator host machine.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%
@@ -321,7 +341,7 @@ At last, note that the two solver algorithms have been executed with the Simgrid
 \label{sec:expe}
 
 
-\subsection{Setup study and Methodology}
+\subsection{Study setup and Simulation Methodology}
 
 To conduct our study, we have put in place the following methodology
 which can be reused for any grid-enabled applications.
@@ -332,7 +352,7 @@ have been chosen for the study in this paper. \\
 
 \textbf{Step 2} : Collect the software materials needed for the
 experimentation. In our case, we have two variants algorithms for the
-resolution of three 3D-Poisson problem: (1) using the classical GMRES (Algo-1)(2) and the multisplitting method (Algo-2). In addition, Simgrid simulator has been chosen to simulate the behaviors of the
+resolution of the 3D-Poisson problem: (1) using the classical GMRES (Algo-1); (2) and the multisplitting method (Algo-2). In addition, Simgrid simulator has been chosen to simulate the behaviors of the
 distributed applications. Simgrid is running on the Mesocentre datacenter in Franche-Comte University but also in a virtual machine on a laptop. \\
 
 \textbf{Step 3} : Fix the criteria which will be used for the future
@@ -341,20 +361,19 @@ in one hand the algorithm execution mode (synchronous and asynchronous)
 and in the other hand the execution time and the number of iterations of
 the application before obtaining the convergence. \\
 
-\textbf{Step 4 }: Setup up the different grid testbeds environment
+\textbf{Step 4 }: Set up the different grid testbed environments
 which will be simulated in the simulator tool to run the program. The
 following architecture has been configured in Simgrid : 2x16 - that is a
 grid containing 2 clusters with 16 hosts (processors/cores) each -, 4x8,
 4x16, 8x8 and 2x50. The network has been designed to operate with a
-bandwidth equals to 10Gbits (resp. 1Gbits/s) and a latency of 8E-6
-microseconds (resp. 5E-5) for the intra-clusters links (resp.
+bandwidth equals to 10Gbits (resp. 1Gbits/s) and a latency of 8.10$^{-6}$
+microseconds (resp. 5.10$^{-5}$) for the intra-clusters links (resp.
 inter-clusters backbone links). \\
 
 \textbf{Step 5}: Conduct an extensive and comprehensive testings
 within these configurations in varying the key parameters, especially
 the CPU power capacity, the network parameters and also the size of the
-input matrix. Note that some parameters should be fixed to be invariant to allow the
-comparison like some program input arguments. \\
+input matrix. Note that some parameters like some program input arguments should be fixed to be invariant to allow the comparison. \\
 
 \textbf{Step 6} : Collect and analyze the output results.
 
@@ -380,7 +399,7 @@ data from a source and the final time the destination have finished to
 receive it. Upon the network characteristics, another impacting factor
 is the application dependent volume of data exchanged between the nodes
 in the cluster and between distant clusters. Large volume of data can be
-transferred in transit between the clusters and nodes during the code
+transferred and transit between the clusters and nodes during the code
 execution.
 
  In a grid environment, it is common to distinguish in one hand, the
@@ -413,7 +432,7 @@ and our comments.\\
 
 
 \textit{3.a Executing the algorithms on various computational grid
-architecture scaling up the input matrix size}
+architecture and scaling up the input matrix size}
 \\
 
 % environment
@@ -434,8 +453,7 @@ Table 1 : Clusters x Nodes with N$_{x}$=150 or N$_{x}$=170 \\
 %\RCE{J'ai voulu mettre les tableaux des donnÃ©es mais je pense que c'est inutile et Ã§a va surcharger}
 
 
-The results in figure 3 show the non-variation of the number of
-iterations of classical GMRES for a given input matrix size; it is not
+In this section, we compare the algorithms performance running on various grid configuration (2x16, 4x8, 4x16 and 8x8). First, the results in figure 3 show for all grid configuration the non-variation of the number of iterations of classical GMRES for a given input matrix size; it is not
 the case for the multisplitting method.
 
 %\begin{wrapfigure}{l}{100mm}
@@ -447,15 +465,13 @@ the case for the multisplitting method.
 \end{figure}
 %\end{wrapfigure}
 
-Unless the 8x8 cluster, the time
-execution difference between the two algorithms is important when
+The execution time difference between the two algorithms is important when
 comparing between different grid architectures, even with the same number of
 processors (like 2x16 and 4x8 = 32 processors for example). The
 experiment concludes the low sensitivity of the multisplitting method
-(compared with the classical GMRES) when scaling up to higher input
-matrix size.
+(compared with the classical GMRES) when scaling up the number of the processors in the grid: in average, the GMRES (resp. Multisplitting) algorithm performs 40\% better (resp. 48\%) less when running from 2x16=32 to 8x8=64 processors.
 
-\textit{\\3.b Running on various computational grid architecture\\}
+\textit{\\3.b Running on two different speed cluster inter-networks\\}
 
 % environment
 \begin{footnotesize}
@@ -482,11 +498,11 @@ Table 2 : Clusters x Nodes - Networks N1 x N2 \\
 %\end{wrapfigure}
 
 The experiments compare the behavior of the algorithms running first on
-a speed inter- cluster network (N1) and a less performant network (N2).
+a speed inter- cluster network (N1) and also on a less performant network (N2).
 Figure 4 shows that end users will gain to reduce the execution time
 for both algorithms in using a grid architecture like 4x16 or 8x8: the
 performance was increased in a factor of 2. The results depict also that
-when the network speed drops down, the difference between the execution
+when the network speed drops down (12.5\%), the difference between the execution
 times can reach more than 25\%.
 
 \textit{\\3.c Network latency impacts on performance\\}
@@ -547,11 +563,8 @@ Table 4 : Network bandwidth impact \\
 
 
 
-The results of increasing the network bandwidth depict the improvement
-of the performance by reducing the execution time for both of the two
-algorithms (Figure 6). However, and again in this case, the multisplitting method
-presents a better performance in the considered bandwidth interval with
-a gain of 40\% which is only around 24\% for classical GMRES.
+The results of increasing the network bandwidth show the improvement
+of the performance for both of the two algorithms by reducing the execution time (Figure 6). However, and again in this case, the multisplitting method presents a better performance in the considered bandwidth interval with a gain of 40\% which is only around 24\% for classical GMRES.
 
 \textit{\\3.e Input matrix size impacts on performance\\}
 
@@ -651,7 +664,7 @@ The test conditions are summarized in the table below : \\
 \begin{tabular}{r c }
  \hline
  Grid & 2x50 totaling 100 processors\\ %\hline
- Processors & 1 GFlops to 1.5 GFlops\\
+ Processors Power & 1 GFlops to 1.5 GFlops\\
    Intra-Network & bw=1.25 Gbits - lat=5.10$^{-5}$ \\ %\hline
    Inter-Network & bw=5 Mbits - lat=2.10$^{-2}$\\
  Input matrix size & N$_{x}$ = From 62 to 150\\ %\hline
@@ -712,8 +725,7 @@ CONCLUSION
 
 \section*{Acknowledgment}
 
-
-The authors would like to thank\dots{}
+This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
 
 
 \bibliographystyle{wileyj}
