Fault tolerance in hypercube-derivative networks
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Fault tolerance in hypercube-derivative networks (preliminary version)
ACM SIGARCH Computer Architecture News - Symposium on parallel algorithms and architectures
IEEE Transactions on Parallel and Distributed Systems
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WE PROPOSE A GRAPH-THEORETIC FRAMEWORK FOR COMPARING THE COMMUNICATION POWERS OF COMPETING INTERCONNECTION NETWORKS BY SEEING HOW EFFICIENTLY ONE OF THE NETWORKS CAN SIMULATE THE OTHER `ON GENERAL COMPUTATIONS''. WITHIN THIS FRAMEWORK, WE PRESENT NEW, SURPRISINGLY EFFICIENT SIMULATIONS BY SHUFFLE-ORIENTED NETWORKS (SUCH AS THE SHUFFLE-EXCHANGE AND DE BRUIJN NET- WORKS) OF `LIKE-SIZED'' BUTTERFLY-ORIENTED NETWORKS (SUCH AS THE BUTTERFLY AND CUBE-CONNECTED-CYCLES NETWORKS): THESE SIMULATIONS INCUR A SLOWDOWN THAT IS `DOUBLY'' LOGARITHMIC IN THE SIZE OF THE SIMULATED NETWORK, HENCE, EXPONENTIALLY FASTER THAN THE ANTICIPATED LOGARITHMIC SLOWDOWN. THE SIMULA- TION MAPPINGS, WHICH CAN BE COMPUTED IN LINEAR TIME, ALSO AFFORD ONE AN ALGORITHMIC TECHNIQUE FOR TRANSLATING PROGRAMS DEVELOPED FOR BUTTERFLY- ORIENTED ARCHITECTURES INTO EQUIVALENT PROGRAMS FOR SHUFFLE-ORIENTED ARCHI- TECHTURES, THE LATTER PROGRAMS INCURRING ONLY THE INDICATED SLOWDOWN FAC- TOR. ONE APPLICATION OF SUCH PROGRAM MAPPING IS A DEMONSTRATION THAT AN ARCHITECTURE BASED ON THE DE BRUIJN NETWORK CAN SIMULATE THE HYPERCUBE ON ANY ASCEND-DESCEND ALGORITHM WITH NO TIME LOSS.