An Input/Output Algorithm for M-Dimensional Rectangular Domain Decompositions on N-Dimensional Hypercube Multicomputers

Hypercube-topology concurrent multicomputers owe at least part of their popularity to the fact that it is relatively simple to decompose rectangularly-shaped Mdimensional domains into subdomains and assign these subdoniains to processors (PES) in a manner which preserves the adjacencies of the subdoniains. However, this decomposition involves some rearrangement of the data during input/output operations to (linear memory) data acquisition, display, or mass storage devices. We show that this rearrangement can be done efficiently, in parallel. The main consequence of this algorithm is that Mdimensional data can be stored in a simple, general format and yet be communicated efaiciently independent of the dimension of the hypercube or the number of these dimensions assigned to the dimensions of the domain. This algorithm is also relevant to applications with mixed domain decompositions, and to parallel mass storage media such as disk farms.