X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/db33461e614769b3c7c7a8239ebf75a014ec3041..380e5cf3507605371bba52eb9a64a9e9c6bcdf24:/loba-besteffort/loba-besteffort.tex

diff --git a/loba-besteffort/loba-besteffort.tex b/loba-besteffort/loba-besteffort.tex
index d774cce..e966c40 100644
--- a/loba-besteffort/loba-besteffort.tex
+++ b/loba-besteffort/loba-besteffort.tex
@@ -27,6 +27,9 @@
 
 \newcommand{\VAR}[1]{\textit{#1}}
 
+\newcommand{\besteffort}{\emph{best effort}}
+\newcommand{\makhoul}{\emph{Makhoul}}
+
 \begin{document}
 
 \begin{frontmatter}
@@ -42,11 +45,13 @@
 \author{Arnaud Giersch\corref{cor}}
 \ead{arnaud.giersch@femto-st.fr}
 
-\address{FEMTO-ST, University of Franche-ComtÃ©\\
- 19 avenue de MarÃ©chal Juin, BP 527, 90016 Belfort cedex , France\\
-  % Tel.: +123-45-678910\\
-  % Fax: +123-45-678910\\
-}
+\address{%
+  Institut FEMTO-ST (UMR 6174),
+  UniversitÃ© de Franche-ComtÃ© (UFC),
+  Centre National de la Recherche Scientifique (CNRS),
+  Ãcole Nationale SupÃ©rieure de MÃ©canique et des Microtechniques (ENSMM),
+  UniversitÃ© de Technologie de Belfort MontbÃ©liard (UTBM)\\
+  19 avenue du MarÃ©chal Juin, BP 527, 90016 Belfort cedex, France}
 
 \cortext[cor]{Corresponding author.}
 
@@ -57,7 +62,7 @@
   the most well known algorithm for which the convergence proof is given. From a
   practical point of view, when a node wants to balance a part of its load to
   some of its neighbors, the strategy is not described.  In this paper, we
-  propose a strategy called \emph{best effort} which tries to balance the load
+  propose a strategy called \besteffort{} which tries to balance the load
   of a node to all its less loaded neighbors while ensuring that all the nodes
   concerned by the load balancing phase have the same amount of load.  Moreover,
   asynchronous iterative algorithms in which an asynchronous load balancing
@@ -104,7 +109,7 @@ Although  the Bertsekas  and Tsitsiklis'  algorithm describes  the  condition to
 ensure the convergence,  there is no indication or  strategy to really implement
 the load distribution. In other word, a node  can send a part of its load to one
 or   many  of   its  neighbors   while  all   the  convergence   conditions  are
-followed. Consequently,  we propose a  new strategy called  \emph{best effort}
+followed. Consequently,  we propose a  new strategy called  \besteffort{}
 that tries to balance the load of  a node to all its less loaded neighbors while
 ensuring that all the nodes concerned  by the load balancing phase have the same
 amount of  load.  Moreover, when real asynchronous  applications are considered,
@@ -213,12 +218,12 @@ algorithm.
 \label{sec.besteffort}
 
 In this section we describe a new load-balancing strategy that we call
-\emph{best effort}.  First, we explain the general idea behind this strategy,
+\besteffort{}.  First, we explain the general idea behind this strategy,
 and then we describe some variants of this basic strategy.
 
 \subsection{Basic strategy}
 
-The general idea behind the \emph{best effort} strategy is that each processor,
+The general idea behind the \besteffort{} strategy is that each processor,
 that detects it has more load than some of its neighbors, sends some load to the
 most of its less loaded neighbors, doing its best to reach the equilibrium
 between those neighbors and himself.
@@ -292,7 +297,7 @@ Section~\ref{sec.results}.  The amount of data to send is then $s_{ij}(t) =
 Another load balancing strategy, working under the same conditions, was
 previously developed by Bahi, Giersch, and Makhoul in
 \cite{bahi+giersch+makhoul.2008.scalable}.  In order to assess the performances
-of the new \emph{best effort}, we naturally chose to compare it to this anterior
+of the new \besteffort{}, we naturally chose to compare it to this anterior
 work.  More precisely, we will use the algorithm~2 from
 \cite{bahi+giersch+makhoul.2008.scalable} and, in the following, we will
 reference it under the name of Makhoul's.
@@ -504,7 +509,7 @@ we will describe in this section.
 \subsubsection{Load balancing strategies}
 
 Several load balancing strategies were compared.  We ran the experiments with
-the \emph{Best effort}, and with the \emph{Makhoul} strategies.  \emph{Best
+the \besteffort{}, and with the \makhoul{} strategies.  \emph{Best
   effort} was tested with parameter $k = 1$, $k = 2$, and $k = 4$.  Secondly,
 each strategy was run in its two variants: with, and without the management of
 \emph{virtual load}.  Finally, we tested each configuration with \emph{real},
@@ -512,7 +517,7 @@ and with \emph{integer} load.
 
 To summarize the different load balancing strategies, we have:
 \begin{description}
-\item[\textbf{strategies:}] \emph{Makhoul}, or \emph{Best effort} with $k\in
+\item[\textbf{strategies:}] \makhoul{}, or \besteffort{} with $k\in
   \{1,2,4\}$
 \item[\textbf{variants:}] with, or without virtual load
 \item[\textbf{domain:}] real load, or integer load
@@ -603,6 +608,7 @@ Anyway, all these the experiments represent more than 240 hours of computing
 time.
 
 \subsubsection{Metrics}
+\label{sec.metrics}
 
 In order to evaluate and compare the different load balancing strategies we had
 to define several metrics.  Our goal, when choosing these metrics, was to have
@@ -647,7 +653,7 @@ With these constraints in mind, we defined the following metrics:
 \label{sec.results}
 
 In this section, the results for the different simulations will be presented,
-and we'll try to explain our observations.
+and we will try to explain our observations.
 
 \subsubsection{Cluster vs grid platforms}
 
@@ -661,7 +667,7 @@ Nevertheless their relative performances remain generally identical.
 This suggests that the relative performances of the different strategies are not
 influenced by the characteristics of the physical platform.  The differences in
 the convergence times can be explained by the fact that on the grid platforms,
-distant sites are interconnected by links of smaller bandwith.
+distant sites are interconnected by links of smaller bandwidth.
 
 Therefore, in the following, we'll only discuss the results for the grid
 platforms.
@@ -700,7 +706,7 @@ initially on an only node, while the results on figure~\ref{fig.resultsN} are
 when the load to balance is initially randomly distributed over all nodes.
 
 On both figures, the computation/communication cost ratio is $10/1$ on the left
-column, and $1/10$ on the right column.  With a computatio/communication cost
+column, and $1/10$ on the right column.  With a computation/communication cost
 ratio of $1/1$ the results are just between these two extrema, and definitely
 don't give additional information, so we chose not to show them here.
 
@@ -708,62 +714,98 @@ On each of the figures~\ref{fig.results1} and~\ref{fig.resultsN}, the results
 are given for the process topology being, from top to bottom, a line, a torus or
 an hypercube.
 
-\FIXME{explain how to read the graphs}
+Finally, on the graphs, the vertical bars show the measured times for each of
+the algorithms.  These measured times are, from bottom to top, the average idle
+time, the average convergence date, and the maximum convergence date (see
+Section~\ref{sec.metrics}).  The measurements are repeated for the different
+platform sizes.  Some bars are missing, specially for large platforms.  This is
+either because the algorithm did not reach the convergence state in the
+allocated time, or because we simply decided not to run it.
 
-each bar -> times for an algorithm
-recall the different times
-no bar -> not run or did not converge in allocated time
+\FIXME{annoncer le plan de la suite}
 
-repeated for the different platform sizes.
+\subsubsection{The \besteffort{} strategy with the load initially on only one
+  node}
 
-\FIXME{donner les premiÃ¨res conclusions, annoncer le plan de la suite}
+Before looking  at the different variations,  we will first show  that the plain
+\besteffort{}  strategy  is valuable,  and  may be  as  good  as the  \makhoul{}
+strategy.  On  the graphs  from the figure~\ref{fig.results1},  these strategies
+(with virtual load feature) are respectively labeled ``b'' and ``a''.
 
-\subsubsection{With the virtual load extension}
+We  can  see  that  the  relative  performance of  these  strategies  is  mainly
+influenced by  the application topology.  It  is for the line  topology that the
+difference is the  more important.  In this case,  the \besteffort{} strategy is
+nearly twice as  fast as the \makhoul{} strategy.  This can  be explained by the
+fact that the \besteffort{} strategy tries to distribute the load faitly between
+all the nodes  and with the line topology,  it is easy to load  balance the load
+fairly.
 
-\subsubsection{The $k$ parameter}
+On the contrary, for the hypercube topology, the \besteffort{} strategy performs
+worse than the \makhoul{} strategy. In this case, the \makhoul{} strategy which
+tries to give more load to few neighbors reaches the equilibrum faster.
 
-\subsubsection{With an initial random repartition,  and larger platforms}
+For the torus  topology, for which the  number of links is between  the line and
+the hypercube, the \makhoul{} strategy  is slightly better but the difference is
+more nuanced.
 
-\subsubsection{With integer load}
+Globally   the  number  of   interconnection  is   very  important.    The  more
+interconnection links there are, the  faster the \makhoul{} strategy is because
+it distributes quickly significant amount of load even if this is unfair between
+all the  neighbors.  In opposition,  the \besteffort{} strategy  distributes the
+load fairly so this strategy is better for low connected strategy.
 
-\FIXME{what about the amount of data?}
 
-\begin{itshape}
-\FIXME{remove that part}
-Dans cet ordre:
-...
-- comparer be/makhoul -> be tient la route
-        -> en rÃ©el uniquement
-- valider l'extension virtual load -> c'est 'achement bien
-- proposer le -k -> Ã§a peut aider dans certains cas
-- conclure avec la version entiÃ¨re -> on n'a pas l'effet d'escalier !
-Q: comment inclure les types/tailles de platesformes ?
-Q: comment faire des moyennes ?
-Q: comment introduire les distrib 1/N ?
-...
+\subsubsection{With the virtual load extension with the load initially on only
+  one node}
 
-On constate quoi (vÃ©rifier avec les chiffres)?
-\begin{itemize}
-\item cluster ou grid, entier ou rÃ©el, ne font pas de grosses diffÃ©rences
+Dans ce cas lÃ©gÃ¨re amÃ©lioration de la cvg. max.  Temps moyen de cvg. amÃ©liorÃ©,
+mais plus de temps passÃ© en idle, surtout quand les comms coutent cher.
 
-\item bookkeeping? amÃ©liore souvent les choses, parfois au prix d'un retard au dÃ©marrage
+\subsubsection{The \besteffort{} strategy with an initial random load
+  distribution, and larger platforms}
 
-\item makhoul? se fait battre sur les grosses plateformes
+MÃªmes conclusions pour line et hcube.
+Sur tore, BE se fait exploser quand les comms coutent cher.
 
-\item taille de plateforme?
+\FIXME{virer les 1024 ?}
 
-\item ratio comp/comm?
+\subsubsection{With the virtual load extension with an initial random load
+  distribution}
 
-\item option $k$? peut-Ãªtre intÃ©ressant sur des plateformes fortement interconnectÃ©es (hypercube)
+Soit c'est Ã©quivalent, soit on gagne -> surtout quand les comms coutent cher et
+qu'il y a beaucoup de voisins.
 
-\item volume de comm? souvent, besteffort/plain en fait plus. pourquoi?
+\subsubsection{The $k$ parameter}
+\label{results-k}
 
-\item rÃ©partition initiale de la charge ?
+Dans le cas oÃ¹ les comms coutent cher et ou BE se fait avoir, on peut ameliorer
+les perfs avec le param k.
 
-\item integer mode sur topo. line n'a jamais fini en plain? vÃ©rifier si ce n'est
-  pas Ã  cause de l'effet d'escalier que bk est capable de gommer.
+\subsubsection{With integer load, 1 ou N}
 
-\end{itemize}
+Cas normal, ligne -> converge pas (effet d'escalier).
+Avec vload, Ã§a converge.
+
+Dans les autres cas, rÃ©sultats similaires au cas rÃ©el: redire que vload est
+intÃ©ressant.
+
+\FIXME{virer la metrique volume de comms}
+
+\FIXME{ajouter une courbe ou on voit l'Ã©volution de la charge en fonction du
+  temps : avec et sans vload}
+
+% \begin{itemize}
+% \item cluster ou grid, entier ou rÃ©el, ne font pas de grosses diffÃ©rences
+% \item bookkeeping? amÃ©liore souvent les choses, parfois au prix d'un retard au dÃ©marrage
+% \item makhoul? se fait battre sur les grosses plateformes
+% \item taille de plateforme?
+% \item ratio comp/comm?
+% \item option $k$? peut-Ãªtre intÃ©ressant sur des plateformes fortement interconnectÃ©es (hypercube)
+% \item volume de comm? souvent, besteffort/plain en fait plus. pourquoi?
+% \item rÃ©partition initiale de la charge ?
+% \item integer mode sur topo. line n'a jamais fini en plain? vÃ©rifier si ce n'est
+%   pas Ã  cause de l'effet d'escalier que bk est capable de gommer.
+% \end{itemize}}
 
 % On veut montrer quoi ? :
 
@@ -790,13 +832,12 @@ On constate quoi (vÃ©rifier avec les chiffres)?
 % Prendre un rÃ©seau hÃ©tÃ©rogÃ¨ne et rendre processeur homogÃ¨ne
 
 % Taille : 10 100 trÃ¨s gros
-\end{itshape}
 
 \section{Conclusion and perspectives}
 
 \FIXME{conclude!}
 
-\section*{Acknowledgements}
+\section*{Acknowledgments}
 
 Computations have been performed on the supercomputer facilities of the
 MÃ©socentre de calcul de Franche-ComtÃ©.
@@ -814,7 +855,10 @@ MÃ©socentre de calcul de Franche-ComtÃ©.
 %%% ispell-local-dictionary: "american"
 %%% End:
 
-% LocalWords:  RaphaÃ«l Couturier Arnaud Giersch Abderrahmane Sider Franche ij
-% LocalWords:  Bertsekas Tsitsiklis SimGrid DASUD ComtÃ© BÃ©jaÃ¯a asynchronism ji
-% LocalWords:  ik isend irecv CortÃ©s et al chan ctrl fifo Makhoul GFlop xml pre
-% LocalWords:  FEMTO Makhoul's fca bdee cdde Contassot Vivier underlaid
+% LocalWords:  RaphaÃ«l Couturier Arnaud Giersch Franche ij Bertsekas Tsitsiklis
+% LocalWords:  SimGrid DASUD ComtÃ© asynchronism ji ik isend irecv CortÃ©s et al
+% LocalWords:  chan ctrl fifo Makhoul GFlop xml pre FEMTO Makhoul's fca bdee
+% LocalWords:  cdde Contassot Vivier underlaid du de MarÃ©chal Juin cedex calcul
+% LocalWords:  biblio Institut UMR UniversitÃ© UFC Centre Scientifique CNRS des
+% LocalWords:  Ãcole Nationale SupÃ©rieure MÃ©canique Microtechniques ENSMM UTBM
+% LocalWords:  Technologie Bahi
