-Load balancing algorithms are extensively used in parallel and distributed
-applications in order to reduce the execution times. They can be applied in
-different scientific fields from high performance computation to micro sensor
-networks. They are iterative by nature. In literature many kinds of load
-balancing algorithms have been studied. They can be classified according
-different criteria: centralized or decentralized, in static or dynamic
-environment, with homogeneous or heterogeneous load, using synchronous or
-asynchronous iterations, with a static topology or a dynamic one which evolves
-during time. In this work, we focus on asynchronous load balancing algorithms
-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 \emph{ping-pong} effect, an asynchronous
-iterative algorithm converge to the uniform load distribution. This work has
-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}.
-\FIXME{Rajouter des choses ici. Lesquelles ?}
-
-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 \besteffort{}
+Load balancing algorithms are widely used in parallel and distributed
+applications to achieve high performances in terms of response time, throughput and resources usage. They play an important role and arise in various fields ranging from parallel and distributed
+computing systems to wireless sensor networks (WSN).
+The objective of load balancing is to orchestrate the distribution of the global load so that
+the load difference between the computational resources of the network is
+minimized as much as possible. Unfortunately, this problem is known to be {\bf NP-hard} in its
+general form and heuristics are required to achieve sub-optimal solutions but in
+polynomial time complexity.
+
+In this paper, we focus on asynchronous load balancing of non negative real numbers of {\it divisible loads}
+in homogeneous distributed systems. Loads can be divided in arbitrary {\it fine-grain} parallel parts size
+that can be processed independently of each other~\cite{Bharadwaj1996, Drozdowski1998, Casanova2008}. This model of divisible loads arises in
+a wide range of real-world applications. Common examples, among many, include signal processing,
+feature extraction and edge detection in image processing, records search in huge databases,
+average consensus in WSN, pattern search in Big data and so on.
+
+
+In the literature, the problem of load balancing has been formulated and studied in various ways. The first pioneering work is due to Bertsekas and Tsitsiklis~\cite{bertsekas+tsitsiklis.1997.parallel}. Under some specific hypothesis and {\it ping-pong} awareness conditions (see section~\ref{sec.bt-algo} for more details), an asymptotic convergence proof is derived.
+
+
+Although Bertsekas and Tsitsiklis describe the necessary conditions to
+ensure the algorithm's convergence, there is no indication nor any strategy to really implement
+the load distribution.
+Consequently, we propose a new strategy called \besteffort{}
