author = {Hestenes, M. R. and Stiefel, E.},
journal = {Journal of research of the National Bureau of Standards},
pages = {409--436},
- timestamp = {2008-10-07T16:03:39.000+0200},
title = {Methods of conjugate gradients for solving linear systems},
volume = {49},
year = {1952}
}
+@book{BT89,
+ author = {Bertsekas, D. and Tsitsiklis, J.},
+ title = {Parallel and distributed computation, numerical methods},
+ publisher = {Prentice Hall Englewood Cliffs N. J. },
+ volume = {},
+ number = {},
+ pages = {},
+ year = {1989},
+}
+@article{bcvc06:ij,
+author = {Bahi, Jacques and Contassot-Vivier, Sylvain and Couturier, Rapha\"el},
+title = {Performance comparison of parallel programming environments for implementing {AIAC} algorithms},
+journal = {Journal of Supercomputing},
+pages = {227--244},
+volume = {35},
+number = {3},
+year = {2006},
+}
+@article{Calheiros:2011:CTM:1951445.1951450,
+ author = {Calheiros, Rodrigo N. and Ranjan, Rajiv and Beloglazov, Anton and De Rose, Cesar A. F. and Buyya, Rajkumar},
+ title = "{CloudSim: A toolkit for modeling and simulation of cloud computing environments and evaluation of resource provisioning algorithms}",
+ journal = {Softw. Pract. Exper.},
+ volume = {41},
+ number = {1},
+ month = jan,
+ year = {2011},
+ pages = {23--50},
+}
+
+@Electronic{SimGrid,
+ title = {{SimGrid} Website},
+ url = {http://simgrid.org/},
+ key = {SimGrid},
+ year = 2014,
+}
\end{abstract}
-\keywords{Algorithm; distributed; iterative; asynchronous; simulation; simgrid; performance}
+%\keywords{Algorithm; distributed; iterative; asynchronous; simulation; simgrid; performance}
+\keywords{Multisplitting algorithms, Synchronous and asynchronous iterations, SimGrid, Simulation}
\maketitle
\section{Introduction}
The use of multi-core architectures for solving large scientific problems seems to become imperative in a lot of cases.
-Whatever the scale of these architectures (distributed clusters, computational grids, embedded multi-core \ldots) they are generally
-well adapted to execute complexe parallel applications operating on a large amount of data. Unfortunately, users (industrials or scientists),
+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. Unfortunately, users (industrials or scientists),
who need such computational resources, may not have an easy access to such efficient architectures. The cost of using the platform and/or the cost of
-testing and deploying an application are often very important. So, in this context it is difficult to optimize a given application for a given
+testing and deploying an application 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.
+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.
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 simple. It generally involves the division of the problem
processing units. Each processing unit has to
compute an iteration, to send/receive some data dependencies to/from
its neighbors and to iterate this process until the convergence of
-the method. Several well-known methods demonstrate the convergence of these algorithms~\cite{BT89,Bahi07}.
+the method. Several well-known methods demonstrate the convergence of these algorithms~\cite{BT89,bahi07}.
In this processing mode a task cannot begin a new iteration while it
has not received data dependencies 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}. This model presents some advantages and drawbacks that we detail in section 2 but even if the number of iterations required to converge is
-generally greater than for the synchronous case, it appears that the asynchronous iterative scheme can significantly reduce overall execution
-times by suppressing idle times due to synchronizations~(see \cite{Bahi07} for more details).
+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 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
+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 leverage the possibility of testing various platform scenarios.
The main contribution of this paper is to show that the use of a simulation tool (i.e. the SimGrid toolkit~\cite{SimGrid}) in the context of real
-parallel applications (i.e. large linear system solver) can help developers to better tune their application for a given multi-core architecture.
-To show the validity of this approach we first compare the simulated execution of the multisplitting algorithm with the GMRES (Generalized Minimal Residual) solver
-\cite{ref1} 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 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.
+parallel applications (i.e. large linear system solvers) can help developers to better tune their application for a given multi-core architecture.
+To show the validity of this approach we first compare the simulated execution of the multisplitting 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 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 related work on the large-scale multi-core simulation of a real synchronous and asynchronous iterative application.
-This paper is organized as follows. Section 1 \ref{sec:synchro} presents the iteration model we use and more particularly the asynchronous scheme.
-In section \ref{sec:simgrid} the SimGrid simulation toolkit is presented. Section \ref{sec:04} details the different solvers that we use.
-Finally our experimental results are presented in section \ref{sec:expe} followed by some concluding remarks and perspectives.
+This paper is organized as follows. Section~\ref{sec:asynchro} presents the iteration model we use and more particularly the asynchronous scheme.
+In section~\ref{sec:simgrid} the SimGrid simulation toolkit is presented. Section~\ref{sec:04} details the different solvers that we use.
+Finally our experimental results are presented in section~\ref{sec:expe} followed by some concluding remarks and perspectives.
\section{The asynchronous iteration model}
