From: Arnaud Giersch Date: Wed, 1 Jun 2011 09:43:04 +0000 (+0200) Subject: Remplacement: \texttt -> \emph. X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/loba-papers.git/commitdiff_plain/857b46f3102ac8bd783b10f189c18ac937ba7fe2?ds=sidebyside Remplacement: \texttt -> \emph. --- 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.