X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/blobdiff_plain/f1aa5b9dfdd4ecd85ea65ea01584c8c452d8acec..6f094055a651749526b1a469813d41f6c28f83a6:/loba-besteffort/loba-besteffort.tex?ds=inline

diff --git a/loba-besteffort/loba-besteffort.tex b/loba-besteffort/loba-besteffort.tex
index 2d37f5f..c387ad6 100644
--- 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
-(\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.
@@ -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
-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
@@ -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
-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?}
 
@@ -346,7 +346,7 @@ information of the load they will receive, so they can take in into account.
 
 In order to test and validate our approaches, we wrote a simulator
 using the SimGrid
-framework~\cite{simgrid.web,casanova+legrand+quinson.2008.simgrid}.  This
+framework~\cite{simgrid.web,casanova+giersch+legrand+al.2014.simgrid}.  This
 simulator, which consists of about 2,700 lines of C++, allows to run
 the different load-balancing strategies under various parameters, such
 as the initial distribution of load, the interconnection topology, the
@@ -382,7 +382,7 @@ 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
+  framework~\cite{casanova+giersch+legrand+al.2014.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
@@ -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.
 
-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}