Exploiting Partial Replication in Unbalanced Parallel Loop Scheduling on Multicomputers

We consider the problem of scheduling parallel loops whose iterations operate on large array data structures and are characterized by highly varying execution times (unbalanced or non-uniform parallel loops). A general parallel loop implementation template for message-passing distributed-memory multiprocessors (multicomputers) is presented. Assuming that it is impossible to statically determine the distribution of the computational load on the data accessed, the template exploits a hybrid scheduling strategy. The data are partially replicated on the processor's local memories and iterations are statically scheduled until rst load imbalances are detected. At this point an eeective dynamic scheduling technique is adopted to move iterations among nodes holding the same data. Most of the communications needed to implement dynamic load balancing are overlapped with computations, as a very eeective prefetching policy is adopted. The template scales very well, since knowing where data are replicated makes it possible to balance the load without introducing high overheads. In the paper a formal characterization of load imbalance related to a generic problem instance is also proposed. This characterization is used to derive an analytical cost model for the template, and in particular, to tune those parameters of the template that depend on the costs related to the speciic features of the target machine and the speciic problem. The template and the related cost model are validated by experiments conducted on a 128-node nCUBE 2, whose results are reported and discussed.