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In this paper, we consider the problem of scheduling divisible loads onto an heterogeneous star platform, with both heterogeneous computing and communication resources. We consider the case where the workers, after processing the tasks, send back some results to the master processor. This corresponds to a more general framework than the one used in many divisible load papers, where only forward communications are taken into account. To the best of our knowledge, this paper constitutes the first attempt to derive optimality results under this general framework (forward and backward communications, heterogeneous processing and communication resources). We prove that it is possible to derive the optimal solution both for LIFO and FIFO distribution schemes. Nevertheless, the complexity of the general problem remains open: we also show in the paper that the optimal distribution scheme may be neither LIFO nor FIFO.

Scheduling Divisible Loads with Return Messages on Heterogeneous Master-Worker Platforms