A method to increase the size of healthy subcubes set in a hypercube system with node or link failures (Q1848704)

Summary: We considered and analyzed the different cases of node and link-faults in a hypercube multiprocessor. We revealed that, the direct use of sharp product operation is not sufficient to discard only computational part (processor and memory), when only this part of node is faulty. We also showed that in case when some links in communication part (router) incident to a healthy node are faulty, the sharp product operation does not allow to leave the healthy links and the node incident to these links in the set of healthy subcubes. In order to remove this lack we propose in this study the formal procedures with aid of which we can subtract first only the faulty node, excluding the healthy links incident to this node and second only the faulty links, excluding also the healthy nodes incident to these links of such systems.