A Tight Bound on the Number of Channel Faults in Wormhole-Routed Multicomputers

Several fault-tolerant deadlock-free routing algorithms have been proposed recently for worm-hole-routed multicomputers, with the number of faults tolerated by these algorithms varying widely. An important problem, therefore, is that of determining a tight lower bound on the number of channels that must be non-faulty in order for messages to be routed without deadlock among the set of remaining non-faulty processors. This paper establishes this tight lower bound. Speciically, we show that if n processors remain, at least 2n ? 2 channels, physical or virtual, are required.