Zographou: World Scientific and Engineering Academy and Society
Hypercubes, meshes, and tori are well known interconnection networks for parallel computing. The Supercube network is a generalization of the hypercube. The main advantage of this network is that it has the same connectivity and diameter as that of the hypercube without the constraint that the number of nodes be a power of 2. This paper proposes novel algorithms of fault-tolerant meshes and tori embedded in supercubes with node failures. The main results obtained (1) a replacing sequence of a supercube is including approximate to (⌊log2 N⌋ +1) nodes. Therefore, there are O(⌊log2 N⌋) faults, which can be tolerated. (2) The result implies that optimal simulation of mesh and torus in a faulty supercube for balancing the processor and communication link loads at present. According to the result, we can easily port the parallel or distributed algorithms developed for these structures to the supercubes. Therefore, these methods of reconfiguring enable extremely high-speed parallel computation.