On a problem of Yuzvinsky on separating the n-cube
Discrete Mathematics
A new look at fault-tolerant network routing
Information and Computation
Information and Computation
Efficient dispersal of information for security, load balancing, and fault tolerance
Journal of the ACM (JACM)
Fault tolerance in hypercube-derivative networks
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Fast computation using faulty hypercubes
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Running algorithms efficiently on faulty hypercubes
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Coding theory, hypercube embeddings, and fault tolerance
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Global Commutative and Associative Reduction Operations in Faulty SIMD Hypercubes
IEEE Transactions on Computers
Efficient Determination of Maximum Incomplete Subcubes in Hypercubes with Faults
IEEE Transactions on Computers
All-To-All Broadcast and Matrix Multiplication in Faulty SIMD Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Embedding and Reconfiguration of Spanning Trees in Faulty Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Unicast in Hypercubes with Large Number of Faulty Nodes
IEEE Transactions on Parallel and Distributed Systems
Subcube Fault Tolerance in Hypercube Multiprocessors
IEEE Transactions on Computers
Free Dimensions-An Effective Approach to Achieving Fault Tolerance in Hypercubes
IEEE Transactions on Computers
Concurrent Processing of Linearly Ordered Data Structures on Hypercube Multicomputers
IEEE Transactions on Parallel and Distributed Systems
Routing in Modular Fault-Tolerant Multiprocessor Systems
IEEE Transactions on Parallel and Distributed Systems
On Some Global Operations in Faulty SIMD Hypercubes
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Spare processor allocation for fault tolerance in torus-based multicomputers
FTCS '96 Proceedings of the The Twenty-Sixth Annual International Symposium on Fault-Tolerant Computing (FTCS '96)
The maximum dimensional fault-free subcube allocatable in faulty hypercube
ICCCN '95 Proceedings of the 4th International Conference on Computer Communications and Networks
Long paths and cycles in hypercubes with faulty vertices
Information Sciences: an International Journal
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The authors examine the issue of running algorithms on a hypercube which has both node and edge faults, and they assume a worst-case distribution of the faults. It is proven that for any constant c, an n-dimensional hypercube (n-cube) with n/sup c/ faulty components contains a fault-tree subgraph that can implement a large class of hypercube algorithms with only a constant factor slowdown. In addition, the approach yields practical implementations for small numbers of faults. For example, it is shown that any regular algorithm can be implemented on an n-cube that has at most n-1 faults with slowdowns of at most two for computation and at most four for communication. This is the first result showing that an n-cube can tolerate more than O(n) arbitrarily placed faults with a constant factor slowdown.