X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/c3657785d32fb5eb5d056044829cc270f154f7eb..6f6ebdac1613681f5093eb2303424044b5f60f12:/supercomp11/supercomp11.tex

diff --git a/supercomp11/supercomp11.tex b/supercomp11/supercomp11.tex
index 2cc35eb..3a1ec31 100644
--- a/supercomp11/supercomp11.tex
+++ b/supercomp11/supercomp11.tex
@@ -5,17 +5,27 @@
 \usepackage{amsmath}
 \usepackage{courier}
 \usepackage{graphicx}
+\usepackage{url}
+\usepackage[ruled,lined]{algorithm2e}
 
 \newcommand{\abs}[1]{\lvert#1\rvert} % \abs{x} -> |x|
 
+\newenvironment{algodata}{%
+  \begin{tabular}[t]{@{}l@{:~}l@{}}}{%
+  \end{tabular}}
+
+\newcommand{\FIXME}[1]{%
+  \textbf{$\triangleright$\marginpar{\textbf{[FIXME]}}~#1}}
+
+\newcommand{\VAR}[1]{\textit{#1}}
+
 \begin{document}
 
 \title{Best effort strategy and virtual load
   for asynchronous iterative load balancing}
 
 \author{Raphaël Couturier \and
-        Arnaud Giersch \and
-        Abderrahmane Sider
+        Arnaud Giersch
 }
 
 \institute{R. Couturier \and A. Giersch \at
@@ -25,10 +35,6 @@
               \email{%
                 raphael.couturier@univ-fcomte.fr,
                 arnaud.giersch@univ-fcomte.fr}
-           \and
-           A. Sider \at
-              University of Béjaïa, Béjaïa, Algeria \\
-              \email{ar.sider@univ-bejaia.dz}
 }
 
 \maketitle
@@ -79,7 +85,7 @@ been extended by many authors. For example, Cortés et al., with
 DASUD~\cite{cortes+ripoll+cedo+al.2002.asynchronous}, propose a
 version working with integer load.  This work was later generalized by
 the same authors in \cite{cedo+cortes+ripoll+al.2007.convergence}.
-{\bf Rajouter des choses ici}.
+\FIXME{Rajouter des choses ici.}
 
 Although  the Bertsekas  and Tsitsiklis'  algorithm describes  the  condition to
 ensure the convergence,  there is no indication or  strategy to really implement
@@ -91,7 +97,7 @@ ensuring that all the nodes concerned  by the load balancing phase have the same
 amount of  load.  Moreover, when real asynchronous  applications are considered,
 using  asynchronous   load  balancing   algorithms  can  reduce   the  execution
 times. Most of the times, it is simpler to distinguish load information messages
-from  data  migration  messages.  Formers  ones  allows  a  node to  inform  its
+from  data  migration  messages.  Former  ones  allows  a  node to  inform  its
 neighbors of its  current load. These messages are very small,  they can be sent
 quite often.  For example, if an  computing iteration takes  a significant times
 (ranging from seconds to minutes), it is possible to send a new load information
@@ -115,15 +121,15 @@ order  to send a  message, a  latency delays  the sending  and according  to the
 network  performance and  the message  size, the  time of  the reception  of the
 message also varies.
 
-In the  following of this  paper, Section~\ref{BT algo} describes  the Bertsekas
-and Tsitsiklis'  asynchronous load balancing  algorithm. Moreover, we  present a
-possible  problem  in  the  convergence  conditions.   Section~\ref{Best-effort}
-presents the best effort strategy which  provides an efficient way to reduce the
-execution  times. In Section~\ref{Virtual  load}, the  virtual load  mechanism is
-proposed. Simulations allowed to show that both our approaches are valid using a
-quite realistic  model detailed in  Section~\ref{Simulations}. Finally we  give a
-conclusion and some perspectives to this work.
-
+In the following of this paper, Section~\ref{BT algo} describes the Bertsekas
+and Tsitsiklis' asynchronous load balancing algorithm. Moreover, we present a
+possible problem in the convergence conditions.  Section~\ref{Best-effort}
+presents the best effort strategy which provides an efficient way to reduce the
+execution times.  This strategy will be compared with other ones, presented in
+Section~\ref{Other}.  In Section~\ref{Virtual load}, the virtual load mechanism
+is proposed.  Simulations allowed to show that both our approaches are valid
+using a quite realistic model detailed in Section~\ref{Simulations}.  Finally we
+give a conclusion and some perspectives to this work.
 
 
 
@@ -180,7 +186,11 @@ $3$.   If  it  sends  load  to  processor $1$  it  will  not  satisfy  condition
 $x_3^2(t)$.  So we consider that the \emph{ping-pong} condition is probably to
 strong. Currently, we did not try to make another convergence proof without this
 condition or with a weaker condition.
-
+%
+\FIXME{Develop: We have the feeling that such a weaker condition
+  exists, because (it's not a proof, but) we have never seen any
+  scenario that is not leading to convergence, even with LB-strategies
+  that are not fulfilling these two conditions.}
 
 \section{Best effort strategy}
 \label{Best-effort}
@@ -236,24 +246,28 @@ he proceeds as following.
   \end{equation*}
 \end{enumerate}
 
+\FIXME{describe parameter $k$}
+
 \section{Other strategies}
 \label{Other}
 
-\textbf{Question} faut-il décrire les stratégies makhoul et simple ?
+\FIXME{Réécrire en angliche.}
 
-\paragraph{simple} Tentative de respecter simplement les conditions de Bertsekas.
-Parmi les voisins moins chargés que soi, on sélectionne :
-\begin{itemize}
-\item un des moins chargés (vmin) ;
-\item un des plus chargés (vmax),
-\end{itemize}
-puis on équilibre avec vmin en s'assurant que notre charge reste
-toujours supérieure à celle de vmin et à celle de vmax.
+% \FIXME{faut-il décrire les stratégies makhoul et simple ?}
 
-On envoie donc (avec "self" pour soi-même) :
-\[
-    \min\left(\frac{load(self) - load(vmin)}{2}, load(self) - load(vmax)\right)
-\]
+% \paragraph{simple} Tentative de respecter simplement les conditions de Bertsekas.
+% Parmi les voisins moins chargés que soi, on sélectionne :
+% \begin{itemize}
+% \item un des moins chargés (vmin) ;
+% \item un des plus chargés (vmax),
+% \end{itemize}
+% puis on équilibre avec vmin en s'assurant que notre charge reste
+% toujours supérieure à celle de vmin et à celle de vmax.
+
+% On envoie donc (avec "self" pour soi-même) :
+% \[
+%     \min\left(\frac{load(self) - load(vmin)}{2}, load(self) - load(vmax)\right)
+% \]
 
 \paragraph{makhoul} Ordonne les voisins du moins chargé au plus chargé
 puis calcule les différences de charge entre soi-même et chacun des
@@ -273,10 +287,10 @@ use this concept, load balancing messages must be sent using two different kinds
 of  messages:  load information  messages  and  load  balancing messages.   More
 precisely, a node  wanting to send a part  of its load to one  of its neighbors,
 can first send  a load information message containing the load  it will send and
-then it  can send the load  balancing message containing data  to be transfered.
+then it can send the load  balancing message containing data  to be transferred.
 Load information  message are really  short, consequently they will  be received
 very quickly.  In opposition, load  balancing messages are often bigger and thus
-require more time to be transfered.
+require more time to be transferred.
 
 The  concept  of  \texttt{virtual load}  allows  a  node  that received  a  load
 information message to integrate the load that it will receive later in its load
@@ -291,7 +305,9 @@ balancing message.
 Doing  this, we  can  expect a  faster  convergence since  nodes  have a  faster
 information of the load they will receive, so they can take in into account.
 
-\textbf{Question} Est ce qu'on donne l'algo avec virtual load?
+\FIXME{Est ce qu'on donne l'algo avec virtual load?}
+
+\FIXME{describe integer mode}
 
 \section{Simulations}
 \label{Simulations}
@@ -333,14 +349,38 @@ a \emph{receiving thread}, a \emph{computing thread}, and a
 
 \paragraph{Receiving thread} The receiving thread is in charge of
 waiting for messages to come, either on the control channel, or on the
-data channel.  When a message is received, it is pushed in a buffer of
+data channel.  Its behavior is sketched by Algorithm~\ref{algo.recv}.
+When a message is received, it is pushed in a buffer of
 received message, to be later consumed by one of the other threads.
 There are two such buffers, one for the control messages, and one for
 the data messages.  The buffers are implemented with a lock-free FIFO
 \cite{sutter.2008.writing} to avoid contention between the threads.
 
+\begin{algorithm}
+  \caption{Receiving thread}
+  \label{algo.recv}
+  \KwData{
+    \begin{algodata}
+      \VAR{ctrl\_chan}, \VAR{data\_chan}
+      & communication channels (control and data) \\
+      \VAR{ctrl\_fifo}, \VAR{data\_fifo}
+      & buffers of received messages (control and data) \\
+    \end{algodata}}
+  \While{true}{%
+    wait for a message to be available on either \VAR{ctrl\_chan},
+    or \VAR{data\_chan}\;
+    \If{a message is available on \VAR{ctrl\_chan}}{%
+      get the message from \VAR{ctrl\_chan}, and push it into \VAR{ctrl\_fifo}\;
+    }
+    \If{a message is available on \VAR{data\_chan}}{%
+      get the message from \VAR{data\_chan}, and push it into \VAR{data\_fifo}\;
+    }
+  }
+\end{algorithm}
+
 \paragraph{Computing thread} The computing thread is in charge of the
-real load management.  It iteratively runs the following operations:
+real load management.  As exposed in Algorithm~\ref{algo.comp}, it
+iteratively runs the following operations:
 \begin{itemize}
 \item if some load was received from the neighbors, get it;
 \item if there is some load to send to the neighbors, send it;
@@ -349,11 +389,40 @@ real load management.  It iteratively runs the following operations:
 \end{itemize}
 Practically, after the computation, the computing thread waits for a
 small amount of time if the iterations are looping too fast (for
-example, when the current load is zero).
+example, when the current load is near zero).
+
+\begin{algorithm}
+  \caption{Computing thread}
+  \label{algo.comp}
+  \KwData{
+    \begin{algodata}
+      \VAR{data\_fifo} & buffer of received data messages \\
+      \VAR{real\_load} & current load \\
+    \end{algodata}}
+  \While{true}{%
+    \If{\VAR{data\_fifo} is empty and $\VAR{real\_load} = 0$}{%
+      wait until a message is pushed into \VAR{data\_fifo}\;
+    }
+    \While{\VAR{data\_fifo} is not empty}{%
+      pop a message from \VAR{data\_fifo}\;
+      get the load embedded in the message, and add it to \VAR{real\_load}\;
+    }
+    \ForEach{neighbor $n$}{%
+      \If{there is some amount of load $a$ to send to $n$}{%
+        send $a$ units of load to $n$, and subtract it from \VAR{real\_load}\;
+      }
+    }
+    \If{$\VAR{real\_load} > 0.0$}{
+      simulate some computation, whose duration is function of \VAR{real\_load}\;
+      ensure that the main loop does not iterate too fast\;
+    }
+  }
+\end{algorithm}
 
 \paragraph{Load-balancing thread} The load-balancing thread is in
 charge of running the load-balancing algorithm, and exchange the
-control messages.  It iteratively runs the following operations:
+control messages.  As shown in Algorithm~\ref{algo.lb}, it iteratively
+runs the following operations:
 \begin{itemize}
 \item get the control messages that were received from the neighbors;
 \item run the load-balancing algorithm;
@@ -363,15 +432,72 @@ control messages.  It iteratively runs the following operations:
   iterate too fast.
 \end{itemize}
 
+\begin{algorithm}
+  \caption{Load-balancing}
+  \label{algo.lb}
+  \While{true}{%
+    \While{\VAR{ctrl\_fifo} is not empty}{%
+      pop a message from \VAR{ctrl\_fifo}\;
+      identify the sender of the message,
+      and update the current knowledge of its load\;
+    }
+    run the load-balancing algorithm to make the decision about load transfers\;
+    \ForEach{neighbor $n$}{%
+      send a control messages to $n$\;
+    }
+    ensure that the main loop does not iterate too fast\;
+  }
+\end{algorithm}
+
+\paragraph{}
+For the sake of simplicity, a few details were voluntary omitted from
+these descriptions.  For an exhaustive presentation, we refer to the
+actual source code that was used for the experiments%
+\footnote{As mentioned before, our simulator relies on the SimGrid
+  framework~\cite{casanova+legrand+quinson.2008.simgrid}.  For the
+  experiments, we used a pre-release of SimGrid 3.7 (Git commit
+  67d62fca5bdee96f590c942b50021cdde5ce0c07, available from
+  \url{https://gforge.inria.fr/scm/?group_id=12})}, and which is
+available at
+\url{http://info.iut-bm.univ-fcomte.fr/staff/giersch/software/loba.tar.gz}.
+
+\FIXME{ajouter des détails sur la gestion de la charge virtuelle ?}
+
 \subsection{Experimental contexts}
 \label{Contexts}
 
-\textbf{FIXME once the experimentations are done!}
+In order to assess the performances of our algorithms, we ran our
+simulator with various parameters, and extracted several metrics, that
+we will describe in this section.  Overall, the experiments represent
+more than 240 hours of computing time.
+
+\paragraph{Load balancing strategies}
+
+We ran the experiments with the \emph{Best effort}, and with the \emph{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}, and with \emph{integer} load.
+This gives us as many as 32 different strategies.
+
+\paragraph{Configurations}
+\begin{description}
+\item[\textbf{platforms}] homogeneous (cluster); heterogeneous (subset
+  of Grid5000)
+\item[\textbf{platform size}] platforms with 16, 64, 256, and 1024 nodes
+\item[\textbf{topologies}] line; torus; hypercube
+\item[\textbf{initial load distribution}] initially on a only node;
+  initially on all nodes
+\item[\textbf{comp/comm ratio}] $10/1$, $1/1$, $1/10$
+\end{description}
+
+\paragraph{Metrics}
+
 \begin{description}
-\item[platforms] homogeneous ; heterogeneous generated with the SIMULACRUM tool~\cite{QUINSON:2010:INRIA-00502839:1}
-\item[topologies]
-\item[algorithms]
-\item[etc.]
+\item[\textbf{average idle time}]
+\item[\textbf{average convergence date}]
+\item[\textbf{maximum convergence date}]
+\item[\textbf{data transfer amount}] relative to the total data amount
 \end{description}
 
 \subsection{Validation of our approaches}
@@ -407,6 +533,10 @@ Taille : 10 100 très gros
 
 \section{Conclusion and perspectives}
 
+\begin{acknowledgements}
+  Computations have been performed on the supercomputer facilities of
+  the Mésocentre de calcul de Franche-Comté.
+\end{acknowledgements}
 
 \bibliographystyle{spmpsci}
 \bibliography{biblio}
@@ -416,9 +546,10 @@ Taille : 10 100 très gros
 %%% Local Variables:
 %%% mode: latex
 %%% TeX-master: t
+%%% fill-column: 80
 %%% ispell-local-dictionary: "american"
 %%% End:
 
 % LocalWords:  Raphaël Couturier Arnaud Giersch Abderrahmane Sider Franche ij
 % LocalWords:  Bertsekas Tsitsiklis SimGrid DASUD Comté Béjaïa asynchronism ji
-% LocalWords:  ik isend irecv
+% LocalWords:  ik isend irecv Cortés et al chan ctrl fifo