Generalized multipartitioning for multi-dimensional arrays

Multipartitioning is a strategy for parallelizing computations that require solving 1D recurrences along each dimension of a multi-dimensional array. Previous techniques for multipartitioning yield efficient parallelizations over 3D domains only when the number of processors is a perfect square. This paper considers the general problem of computing multipartitionings for d-dimensional data volumes on an arbitrary number of processors. We describe an algorithm that computes an optimal multipartitioning onto all of the processors for this general case. Finally, we describe how we extended the Rice dHPF compiler for High Performance Fortran to generate code that exploits generalized multipartitioning and show that the compiler’s generated code for the NAS SP computational fluid dynamics benchmark achieves scalable high performance. 1