DC Transpose: a method for reducing communication in divide-and-conquer algorithms on mesh-based computers

Previous approaches to solving divide-and-conquer algorithms required a number of direct neighbor communications equal to the diameter of the computer. For a k dimensional mesh, this diameter is k ^k√n-k where n is the number of processors. The paper introduces the notion of a DC Transpose, which is a remapping of data on a mesh, using a global routing mechanism such as the global router on the Mas-Par MP-1. With a single DC Transpose, the number of direct neighbor communications is reduced to 2k ^2k√n-2k. DC Transpose and its associated mappings are described, and benchmarks on the MasPar MP-1 are presented