Hypercube Algorithms on the Polymorphic Torus

Abstract

The Polymorphic Torus architecture is a reconfigurable, massively parallel finegrained system, which in its two-dimensional $(N^{2})$ case has a lower wiring complexity than, say, hypercubes. However, due to the dynamic connection features at run-time, it allows several parallel structures such as trees, rings, and hypercubes to be emulated efficiently. In this paper, we consider algorithms that are especially well-suited for hypercubes, i.e. algorithms that take advantage of the relatively high connectivity of the hypercube topology, and show how these algorithms attain comparable bounds on a 2-D Polymorphic Torus. In particular, algorithms for dense matrix vector multiplication (including using 2 orthogonal trees for the matrix-vector case), sparse matrix-vector multiplication, and the FFT are discussed.