Fault-tolerant routing on Complete Josephus Cubes

This paper introduces the Complete Josephus Cube, a fault-tolerant class of the recently proposed Josephus Cube and proposes a cost-effective, fault-tolerant routing strategy for the Complete Josephus Cube. For a Complete Josephus Cube of order r, the routing algorithm can tolerate up to (r+1) encountered component faults in its message path and generates routes that are both deadlock-free and livelock-free. The message is guaranteed to be optimally (respectively, sub-optimally) delivered within a maximum of r (respectively, 2r+1) hops. The message overhead incurred is only a single (r+2)-bit routing vector accompanying the message to be communicated.