From a4d32c2405b3bac006e911ab9fb20910ffb183c9 Mon Sep 17 00:00:00 2001 From: =?utf8?q?S=C3=A9bastien=20Miqu=C3=A9e?= Date: Fri, 22 Jan 2010 15:09:05 +0100 Subject: [PATCH] Correction typos et remise en forme. --- pdsec2010/pdsec2010.aux | 6 +- pdsec2010/pdsec2010.log | 412 ++++++++++++++++++---------------------- pdsec2010/pdsec2010.out | 1 - pdsec2010/pdsec2010.pdf | Bin 396493 -> 387637 bytes pdsec2010/pdsec2010.tex | 151 ++++++++------- 5 files changed, 263 insertions(+), 307 deletions(-) diff --git a/pdsec2010/pdsec2010.aux b/pdsec2010/pdsec2010.aux index fdb9da9..c255b10 100644 --- a/pdsec2010/pdsec2010.aux +++ b/pdsec2010/pdsec2010.aux @@ -29,13 +29,13 @@ \citation{dag1,dag2,dag3,dag4} \citation{tig1,tig2} \newlabel{sec:benef}{{II}{3}{Benefits of mapping\relax }{section*.1}{}} +\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Effects of a simple tasks mapping algorithm on application's execution time}}{3}{table.1}} +\newlabel{tab:benef}{{I}{3}{Effects of a simple tasks mapping algorithm on application's execution time\relax }{table.1}{}} \@writefile{toc}{\contentsline {section}{\numberline {III}Problem description}{3}{section.3}} \newlabel{sec:pb}{{III}{3}{Problem description\relax }{section.3}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {III-A}}Model formalization}{3}{subsection.3.1}} \newlabel{sec:pbmodel}{{\unhbox \voidb@x \hbox {III-A}}{3}{Model formalization\relax }{subsection.3.1}{}} \newlabel{sec:pbmodelapp}{{\unhbox \voidb@x \hbox {III-A}1}{3}{Application modeling\relax }{subsubsection.3.1.1}{}} -\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Effects of a simple tasks mapping algorithm on application's execution time}}{3}{table.1}} -\newlabel{tab:benef}{{I}{3}{Effects of a simple tasks mapping algorithm on application's execution time\relax }{table.1}{}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {\unhbox \voidb@x \hbox {III-A}1}Application modeling}{3}{subsubsection.3.1.1}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces An example of a TIG of a nine tasks application}}{3}{figure.2}} \newlabel{fig:tig}{{2}{3}{An example of a TIG of a nine tasks application\relax }{figure.2}{}} @@ -77,8 +77,6 @@ \@writefile{toc}{\contentsline {subsubsection}{\numberline {\unhbox \voidb@x \hbox {V-B}2}Edge-cuts optimization}{6}{subsubsection.5.2.2}} \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {V-C}}Experiments}{6}{subsection.5.3}} \newlabel{sec:experiments}{{\unhbox \voidb@x \hbox {V-C}}{6}{Experiments\relax }{subsection.5.3}{}} -\newlabel{sec:xphetero}{{\unhbox \voidb@x \hbox {V-C}1}{6}{About heterogeneity\relax }{subsubsection.5.3.1}{}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {\unhbox \voidb@x \hbox {V-C}1}About heterogeneity}{6}{subsubsection.5.3.1}} \@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces Gains in time of the execution of the class E of the CG application on Arc1.1 using 64 nodes}}{7}{table.2}} \newlabel{tab:exph1E}{{II}{7}{Gains in time of the execution of the class E of the CG application on Arc1.1 using 64 nodes\relax }{table.2}{}} \@writefile{lot}{\contentsline {table}{\numberline {III}{\ignorespaces Gains in time of the execution of the class F of the CG application on Arc1.2 using 128 nodes}}{7}{table.3}} diff --git a/pdsec2010/pdsec2010.log b/pdsec2010/pdsec2010.log index de2d8c8..af6a623 100644 --- a/pdsec2010/pdsec2010.log +++ b/pdsec2010/pdsec2010.log @@ -1,18 +1,9 @@ -This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) (format=pdflatex 2009.10.27) 22 JAN 2010 10:58 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2010.1.19) 22 JAN 2010 15:08 entering extended mode + restricted \write18 enabled. %&-line parsing enabled. -**pdsec2010 -(./pdsec2010.tex -LaTeX2e <2005/12/01> -Babel and hyphenation patterns for english, usenglishmax, dumylang, noh -yphenation, 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This allows to reduce at each round the @@ -962,7 +966,7 @@ map the task on nodes that are neighbors of nodes of which the dependencies of $t_i$ are mapped on. This is one of the major modification to the original QM algorithm. It introduces a little part of ``edge-cuts'' optimization. In the original version, it tries to -map the task $t_i$ on the same node of one as its dependencies. As +map the task $t_i$ on the same node of one of its dependencies. As explain in \ref{sec:specAIACmapping}, this is not an acceptable solution in our case. Instead, the algorithm now searches to map task $t_i$ on nodes which are near the ones its dependencies are mapped @@ -980,7 +984,7 @@ considered in this round, $r$ is incremented. The complexity of the AIAC QM algorithm is about $O(n^2 \cdot t \cdot ln(r))$. This complexity is the same as the original algorithm (details are given in \cite{qm_these}, with an increase of a factor -$n$, corresponding to the edge-cuts part. +$n$, corresponding to the edge-cuts part). \section{Experimentation} \label{sec:expe} @@ -1013,11 +1017,11 @@ horizontal rectangle parts. Each of these parts is assigned to a processor -- so the size of data depends on the matrix size but also on the number of participating -nodes. In this way, a processor is in charge of computing its $X Sub$ -part by solving the following subsystem: $ASub \times XSub = BSub - -DepLeft \times XLeft - DepRight \times XRight$ +nodes. In this way, a processor is in charge of computing its {\small $X Sub$} +part by solving the following subsystem: {\small $ASub \times XSub = BSub - +DepLeft \times XLeft - DepRight \times XRight$}. -After solving $XSub$, the result must be sent to other +After solving {\small $XSub$}, the result must be sent to other processors which depend on it. % \begin{figure}[h!] @@ -1059,8 +1063,8 @@ processors which depend on it. For more details about this method, interested readers are invited to see \cite{book_raph}. In our benchmark, the sequential solver part of the multisplitting method is the Conjugate Gradient, using the -MTJ\cite{mtj} library. Its implementation is multi-threaded, so it -benefits from multi-core processors. +MTJ\cite{mtj} library. Its implementation is multi-threaded, to +benefit from multi-core processors. We point out here that this benchmark is a typical AIAC application. In our study, we consider that the computational costs of @@ -1187,6 +1191,8 @@ task is assigned to a particular computing node of the chosen cluster. %on distributed clusters architectures, with a gain over $30\%$ on %execution, as experiments described in section \ref{sec:benef}. +\vspace*{0.2cm} + \subsubsection{Edge-cuts optimization} \label{sec:edgcutalgo} @@ -1354,10 +1360,11 @@ size $5,000,000$ (named ``class F'') using 128 nodes. -\subsubsection{About heterogeneity} -\label{sec:xphetero} +%\subsubsection{About heterogeneity} +%\label{sec:xphetero} -The first experiments concern the study of the impact of the +%The first experiments concern the study of the impact of the +Our experiments concern the study of the impact of the heterogeneity of the computing nodes on the mapping results. Heterogeneity is an important factor in high performance computing in the grid all the more so when using the asynchronous -- 2.39.5