Minor changes.

diff --git a/loba-besteffort/loba-besteffort.tex b/loba-besteffort/loba-besteffort.tex
index 2d37f5f094dfa56c8c7e6f4a9f823b7981c13879..88ad56018a3e826c0ec87b0ad18d60e2dbc3aca4 100644 (file)
--- a/loba-besteffort/loba-besteffort.tex
+++ b/loba-besteffort/loba-besteffort.tex
@@ -200,7 +200,7 @@ chain which 3 processors). Now consider we have the following values at time $t$
 \end{align*}
 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
 \end{align*}
 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
+\eqref{eq.ping-pong} because after the sending it will be less loaded that

 $x_3^2(t)$.  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.
 $x_3^2(t)$.  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.


@@ -317,8 +317,8 @@ neighbor.
 In this section,  we present the concept of \emph{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
 In this section,  we present the concept of \emph{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
+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
 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


@@ -335,7 +335,7 @@ 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
 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.
+information of the load they will receive, so they can take it into account.

 
 \FIXME{Est ce qu'on donne l'algo avec virtual load?}
 
 
 \FIXME{Est ce qu'on donne l'algo avec virtual load?}
 


@@ -560,7 +560,7 @@ algorithms currently do not handle heterogeneous computing resources, the
 processor speeds were normalized, and we arbitrarily chose to fix them to
 1~GFlop/s.
 
 processor speeds were normalized, and we arbitrarily chose to fix them to
 1~GFlop/s.
 

-Then we derived each sort of platform with four different number of computing
+Then we derived each kind of platform with four different numbers of computing

 nodes: 16, 64, 256, and 1024 nodes.
 
 \subsubsection{Configurations}
 nodes: 16, 64, 256, and 1024 nodes.
 
 \subsubsection{Configurations}