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Programming distributed-memory machines requires that the data associated with a given computation be partitioned and distributed to the local storage of each individual processor. How this distribution is done affects the amount of data movement required and, therefore, the program performance. The alignment technique presented here focuses on minimizing the data movement between processors due to cross-references between multiple distributed arrays. It also simplifies, both conceptually and in practice, the task of data partition and communication generation in the context of a parallelizing compiler for distributed-memory machines. The problem of index domain alignment is formulated as finding a set of suitable alignment functions that embed the index domains of the arrays into a common index domain so as to minimize the cost of data movement. The cost function and the machine model used are abstractions of the current generation of SIMD and MIMD distributed-memory machines. The problem as formulated is shown to be NP-complete. A heuristic algorithm is devised and shown to both be efficient and provide excellent results. |
