10 Brett A. Becker 2011 Parallel Computing, Heterogeneous Computing, High Performance Computing, Scientific Computing, Data Partitioning, Matrix-Matrix Multiplication <p>This report presents new data partitioning algorithms for matrix and linear algebra operations. These algorithms would in fact work with little or no modification for any application with similar communication patterns. In practice these partitionings distribute data between a small number of computing entities, each of which can have great computational power themselves, and an even greater aggregate power. These partitionings may also be deployed in a hierarchical manner, which allows the flexibility to be employed in a great range of problem domains and computational platforms. These partitionings, in hybrid form, working together with more traditional partitionings, minimize the total volume of communication between entities in a manner proven to be optimal. This is done regardless of the power ratio that exists between the entities, thus minimizing execution time. There is also no restriction on the algorithms or methods employed on the clusters themselves locally, thus maximizing flexibility. Finally, most heterogeneous algorithms and partitionings are designed by modifying existing homogeneous ones. With this in mind the ultimate contribution of this report is to demonstrate that non-traditional and perhaps unintuitive algorithms and partitionings designed with heterogeneity in mind from the start can result in better, and in many cases optimal, algorithms and partitionings for heterogeneous platforms. The importance of this given the current outlook for, and trends in, the future of high performance scientific computing is obvious.</p>