H-lattice: a geometric model for processor allocation in hypercubes

The H-lattice is a geometric model for describing the construction and occupied configuration of the hypercube multiprocessors. In addition, it can model the faulty hypercube in the presence of faulty processors and/or links. The H-lattice scheme, based on this model, can allocate fault free subcubes for various allocations, such as first/best/worst/next fit, and subcube inclusion/ exclusion allocations, in a more simple and efficient manner than ever. In this scheme, the viewpoint of the minimum destroyed degree is introduced to select the best-fit subcube, which is proved to be better than that of other schemes. Mathematical analyses and simulation are also derived to demonstrate the efficiency of the proposed scheme.