X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/77dfff6971a1d64b3274379ad340410840d24980..616eff22be6d742dbc218943c6901dd2f7a2a9dc:/supercomp11/supercomp11.tex

diff --git a/supercomp11/supercomp11.tex b/supercomp11/supercomp11.tex
index b0d23b0..cb1c983 100644
--- a/supercomp11/supercomp11.tex
+++ b/supercomp11/supercomp11.tex
@@ -5,9 +5,16 @@
 \usepackage{amsmath}
 \usepackage{courier}
 \usepackage{graphicx}
+\usepackage[ruled,lined]{algorithm2e}
 
 \newcommand{\abs}[1]{\lvert#1\rvert} % \abs{x} -> |x|
 
+\newenvironment{algodata}{%
+  \begin{tabular}[t]{@{}l@{:~}l@{}}}{%
+  \end{tabular}}
+
+\newcommand{\VAR}[1]{\textit{#1}}
+
 \begin{document}
 
 \title{Best effort strategy and virtual load
@@ -49,7 +56,7 @@ Moreover,  asynchronous  iterative  algorithms  in which  an  asynchronous  load
 balancing  algorithm is  implemented most  of the  time can  dissociate messages
 concerning load transfers and message  concerning load information.  In order to
 increase  the  converge of  a  load balancing  algorithm,  we  propose a  simple
-heuristic called \emph{virtual load} which allows a node that receives an load
+heuristic called \emph{virtual load} which allows a node that receives a load
 information message  to integrate the  load that it  will receive later  in its
 load (virtually) and consequently sends a (real) part of its load to some of its
 neighbors.  In order to  validate our  approaches, we  have defined  a simulator
@@ -75,9 +82,11 @@ algorithm which is definitively a reference  for many works. In their work, they
 proved that under classical  hypotheses of asynchronous iterative algorithms and
 a  special  constraint   avoiding  \emph{ping-pong}  effect,  an  asynchronous
 iterative algorithm  converge to  the uniform load  distribution. This  work has
-been extended by many authors. For example,
-DASUD~\cite{cortes+ripoll+cedo+al.2002.asynchronous} propose a version working
-with integer load. {\bf Rajouter des choses ici}.
+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}.
 
 Although  the Bertsekas  and Tsitsiklis'  algorithm describes  the  condition to
 ensure the convergence,  there is no indication or  strategy to really implement
@@ -183,12 +192,13 @@ condition or with a weaker condition.
 \section{Best effort strategy}
 \label{Best-effort}
 
-We will describe here a new load-balancing strategy that we called
-\emph{best effort}.  The general idea behind this strategy is, for a
-processor, to send some load to the most of its neighbors, doing its
+In this section we  describe  a new load-balancing strategy that we call
+\emph{best effort}.  The general idea behind this 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.
 
-More precisely, when a processors $i$ is in its load-balancing phase,
+More precisely, when a processor $i$ is in its load-balancing phase,
 he proceeds as following.
 \begin{enumerate}
 \item First, the neighbors are sorted in non-decreasing order of their
@@ -265,6 +275,31 @@ C'est l'algorithme~2 dans~\cite{bahi+giersch+makhoul.2008.scalable}.
 \section{Virtual load}
 \label{Virtual load}
 
+In this section,  we present the concept of \texttt{virtual  load}.  In order to
+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 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 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
+(virtually)  and consequently send  a (real)  part of  its load  to some  of its
+neighbors. In fact,  a node that receives a load  information message knows that
+later it  will receive the  corresponding load balancing message  containing the
+corresponding data.  So  if this node detects it is too  loaded compared to some
+of its neighbors  and if it has enough  load (real load), then it  can send more
+load  to  some of  its  neighbors  without waiting  the  reception  of the  load
+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?
+
 \section{Simulations}
 \label{Simulations}
 
@@ -278,8 +313,9 @@ characteristics of the running platform, etc.  Then several metrics
 are issued that permit to compare the strategies.
 
 The simulation model is detailed in the next section (\ref{Sim
-  model}), then the results of the simulations are presented in
-section~\ref{Results}.
+  model}), and the experimental contexts are described in
+section~\ref{Contexts}.  Then the results of the simulations are
+presented in section~\ref{Results}.
 
 \subsection{Simulation model}
 \label{Sim model}
@@ -304,14 +340,38 @@ 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;
@@ -320,7 +380,35 @@ 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
@@ -334,6 +422,61 @@ 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 code that was used for the experiments, and which is
+available at \textbf{FIXME URL}.
+
+\textbf{FIXME: ajouter des détails sur la gestion de la charge virtuelle ?}
+
+\subsection{Experimental contexts}
+\label{Contexts}
+
+\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{Algorithms}
+\begin{description}
+\item[\textbf{strategies}] makhoul; besteffort with $k\in \{1,2,4\}$
+\item[\textbf{variants}] with, and without virtual load (bookkeeping)
+\item[\textbf{domain}] real load, and integer load
+\end{description}
+
+\paragraph{Metrics}
+
+\begin{description}
+\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}
 \label{Results}
 
@@ -381,4 +524,4 @@ Taille : 10 100 très gros
 
 % 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