Two techniques for static array partitioning on message-passing parallel machines

We present two elegant techniques for partitioning arrays in parallel Do All loops for message-passing parallel machines. (1) Communication-free array partitioning: A general solution of communication-free partitioning is derived for arrays in a DoAll loop. The derivation is based on the Smith Normal Form decomposition of the matrix which characterizes the array references in a DoAll loop. (2) One block-communication partitioning: When communication-free partitioning is not possible, we derive the partitioning equations which allocate all remote data to a unique processor. Thus, at most one block-communication is required for each processor to obtain the remote data it needs during computation.