Mapping nested loops onto distributed memory multiprocessors

The paper presents Chain grouping; a new low complexity method for the problem of partitioning the index space into groups with little intercommunication requirements, for mapping onto distributed mesh connected architectures. First the loop iterations are scheduled in time, according to the hyperplane method, taking into consideration the minimum time displacement. Then, the index space is divided into discrete groups of related computations, which are assigned to different processors, while preserving the optimal makespan. The Chain grouping method is based on grouping along a uniform chain of computations, formed by a particular dependence vector. This vector will be proved as the best to reduce the total communication requirements. Inside every group, the optimal hyperplane scheduling is preserved, and the references to intragroup computations are considerably increased. The partitioned groups are afterwards assigned to meshes of processors. The resulting space mapping maximises processor utilisation and cuts down overall communication delays while preserving the optimal hyperplane time schedule.