Loop partitioning unimodular transformations for distributed memory multiprocessors

Presents a unimodular transformation called rotation to partition the iteration space of a perfectly nested loop. The transformation captures the individual transformations like loop interchange, reversal, and skewing in a uniform framework. Though the transformation is for any architecture, the authors have specifically addressed its application to distributed memory machines in this paper. The authors prove that the transformation is free from deadlocks. They finally describe the choice of an optimal rotation based on the parallelism factor, load imbalance and the volume of communication in the transformed space