In the recent years, there was a huge development of low cost large scale parallel systems. The design of efficient parallel algorithms has to be reconsidered by the influence of new parameters of such execution supports (namely, clusters of workstations, grid computing and global computing) which are characterized by a larger number of heterogeneous processors, often organized by hierarchical sub-systems. Alternative computational models have been designed in order to take into account new characteristics. Parallel Tasks model -- PT in short -- (i.e. tasks that require more than one processor for their execution) is a promising alternative for scheduling parallel applications, especially in the case of slow communication media. The basic idea is to consider the application at a rough level of granularity. Another way of looking at the problem (which is somehow a dual view) is the Divisible Load model (DL) where an application is considered as a collection of a large number of elementary -- sequential -- computing units that will be distributed among the available resources. As the main difficulty for scheduling in actual systems comes from handling efficiently the communications, these two new views of the problem allow us to consider them implicitly or to mask them, thus leading to more tractable problems. This paper aims first at presenting some examples of approximation algorithms for parallelizing applications for the PT model with a special emphasis on new execution supports. Then, we will show how to mix these results with the DLT model in order to integrate them into the previous model for managing the resources of an actual computational grid composed by more than 600 machines built in Grenoble (CiGri project).
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