X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/69768dd70773e43e60a13d06dad73a65c00dfb85..857b46f3102ac8bd783b10f189c18ac937ba7fe2:/supercomp11/supercomp11.tex

diff --git a/supercomp11/supercomp11.tex b/supercomp11/supercomp11.tex
index 249b676..edf5207 100644
--- a/supercomp11/supercomp11.tex
+++ b/supercomp11/supercomp11.tex
@@ -39,14 +39,14 @@ algorithm~\cite[section~7.4]{bertsekas+tsitsiklis.1997.parallel}
 is certainly  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 \texttt{best effort} which tries to balance
+paper, we propose a strategy  called \emph{best effort} 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  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 \texttt{virtual load} which allows a node that receives an load
+heuristic called \emph{virtual load} which allows a node that receives an 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
@@ -70,7 +70,7 @@ where computer nodes  are considered homogeneous and with  homogeneous load with
 no external  load. In  this context, Bertsekas  and Tsitsiklis have  proposed an
 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  \texttt{ping-pong}  effect,  an  asynchronous
+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
@@ -80,7 +80,7 @@ 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  \texttt{best effort}
+followed. Consequently,  we propose a  new strategy called  \emph{best effort}
 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,
@@ -98,7 +98,7 @@ often much nore longer that to  time to transfer a load information message. So,
 when a node receives the information  that later it will receive a data message,
 it can take this information into account  and it can consider that its new load
 is larger.   Consequently, it can  send a part  of it real  load to some  of its
-neighbors if required. We call this trick the \texttt{virtual load} mecanism.
+neighbors if required. We call this trick the \emph{virtual load} mecanism.
 
 
 
@@ -151,7 +151,7 @@ x_i(t+1)=x_i(t)-\sum_{j\in V(i)} s_{ij}(t) + \sum_{j\in V(i)} r_{ji}(t)
 
 
 Some  conditions are  required to  ensure the  convergence. One  of them  can be
-called the \texttt{ping-pong} condition which specifies that:
+called the \emph{ping-pong} condition which specifies that:
 \begin{equation}
 x_i(t)-\sum _{k\in V(i)} s_{ik}(t) \geq x_j^i(t)+s_{ij}(t)
 \end{equation}
@@ -172,7 +172,7 @@ x_3(t)=99.99\\
 In this case, processor $2$ can  either sends load to processor $1$ or processor
 $3$.   If  it  sends  load  to  processor $1$  it  will  not  satisfy  condition
 (\ref{eq:ping-pong})  because  after the  sending  it  will  be less  loaded  that
-$x_3^2(t)$.  So we consider that the \texttt{ping-pong} condition is probably to
+$x_3^2(t)$.  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.