Alain Darte, John Mellor-Crummey, Robert Fowler, and Daniel Chavarría-Miranda. Generalized multipartitioning. In Proceedings of the Los Alamos Computer Science Institute Second Annual Symposium, Santa Fe, NM, October 2001. [ps] [pdf]

Multipartitioning is a strategy for partitioning multi-dimensional arrays among a collection of processors. With multipartitioning, computations that require solving one-dimensional recurrences along each dimension of a multi-dimensional array can be parallelized effectively. Previous techniques for multipartitioning yield efficient parallelizations over three-dimensional domains only when the number of processors is a perfect square. This paper considers the general problem of computing optimal multipartitionings for d-dimensional data volumes on an arbitrary number of processors. We describe an algorithm that computes an optimal multipartitioning for this general case, which enables multipartitioning to be used for performing efficient parallelizations of line-sweep computations under arbitrary conditions.

Finally, we describe a prototype implementation of generalized multipartitioning in the Rice dHPF compiler and performance results obtained when using it to parallelize a line sweep computation for different numbers of processors.