FIFO scheduling of divisible loads with return messages under the one-port model

This paper deals with scheduling divisible load applications on star networks, in presence of return messages. This work is a follow-on of Beumont et al. (2005), where the same problem was considered under the two-port model, where a given processor can simultaneously send and receive a message. Here, we concentrate on the one-port model, where a processor can either send or receive a message at a given time step. The problem of scheduling divisible load on star platforms turns out to be very difficult as soon as return messages are involved. Unfortunately, we have not been able to assess its complexity, but we provide an optimal solution in the special (but important) case of FIFO communication schemes. We also provide an explicit formula for the optimal number of load units that can be processed by a FIFO ordering on a bus network. Finally, we provide a set of MPI experiments to assess the accuracy and usefulness of our results in a real framework.