Mapping of uniform dependence algorithm onto fixed size processor arrays

The paper addresses the problem of mapping uniform dependence algorithms onto fixed size processor arrays. The optimal computation time of executing uniform dependence algorithm on a fixed size processor array is first discussed. A mapping and partitioning method for 2-dimensional algorithms (algorithms with doubly nested loops) which can achieve near optimal computation time is proposed. Necessary and sufficient conditions are presented for a given pair of schedule and partition to be time optimal. The inefficient utilization of processors is caused by the boundary time steps. For a given pair of schedule and partition vectors, the number of boundary time steps is identified. Also, the amount of external communication, which is the communication between blocks of a partition, by a given pair of schedule and partition vectors is studied. Issues concerning minimizing boundary time steps and external communication are discussed