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\title{Best effort strategy and virtual load for asynchronous iterative load balancing}

\author{Raphaël Couturier \and
        Arnaud Giersch \and
        Abderrahmane Sider
}

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\begin{abstract}

Most of the  time, asynchronous load balancing algorithms  have extensively been
studied in a theoretical point  of view. The Bertsekas and Tsitsiklis'
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
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
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
based on SimGrid which allowed us to conduct many experiments.


\end{abstract}



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  \texttt{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.


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% LocalWords:  Raphaël Couturier Arnaud Giersch Abderrahmane Sider
% LocalWords:  Bertsekas Tsitsiklis SimGrid DASUD
