Job simulation techniques on incomplete and Gray code incomplete hypercubes

We show that any job (in particular, data communication techniques such as sorting, merging, parallel prefix, distribution etc.) can be executed on the synchronous model of incomplete hypercube within asymptotically the same time complexity as on a (complete) hypercube of appropriate size. We then obtain similar results for the GCIH (Gray code incomplete hypercube) model. GCIHs have some applications based on partitioning a (complete) hypercube into several GCIHs, each being temporarily isolated from the rest of hypercube. GCIHs provide a very simple method to allocate some processors to perform a job on a complete hypercube, since it enables the memory allocation techniques for sequential computers to be directly used. The other application is in image processing and other fields where multiple component problems occur