The task management is a critical component for the computational grids. The aim is to assign tasks on nodes according to a global scheduling policy and a view of local resources of nodes. A peer-to-peer approach for the task management involves a better scalability for the grid and a higher fault tolerance. But some mechanisms have to be proposed to avoid the computation of replicated tasks that can reduce the efficiency and increase the load of nodes. In the same way, these mechanisms have to limit the number of exchanged messages to avoid the overload of the network. In a previous paper, we have proposed two methods for the task management called active and passive. These methods are based on a random walk: they are fully distributed and fault tolerant. Each node owns a local tasks states set updated thanks to a random walk and each node is in charge of the local assignment. Here, we propose three methods to improve the efficiency of the active method. These new methods are based on a circulating word. The nodes local tasks states sets are updated thanks to periodical diffusions along trees built from the circulating word. Particularly, we show that these methods increase the efficiency of the active method: they produce less replicated tasks. These three methods are also fully distributed and fault tolerant. On the other way, the circulating word can be exploited for other applications like the resources management or the nodes synchronization.
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