On a problem of Yuzvinsky on separating the n-cube
Discrete Mathematics
A new look at fault-tolerant network routing
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
Embedding meshes in Boolean cubes by graph decomposition
Journal of Parallel and Distributed Computing - Special issue: algorithms for hypercube computers
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Mathematical and Computer Modelling: An International Journal
Embedding and Reconfiguration of Binary Trees in Faulty Hypercubes
IEEE Transactions on Parallel and Distributed Systems
A Fault-Tolerant Tree Communication Scheme for Hypercube Systems
IEEE Transactions on Computers
A Low-Cost Fault-Tolerant Structure for the Hypercube
The Journal of Supercomputing
Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions
IEEE Transactions on Computers
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We examine the issue of running algorithms with a constant factor slowdown on a faulty hypercube in a worst case scenario. We present two sets of novel results related to this issue. We first consider edge faults and show how to tolerate faults with a constant factor slow-down in communication and no slowdown in computation. The key to our approach is an efficient method for embedding a fault free Cube Connected Cycles (CCC) graph in the faulty hypercube. Using this embedding we can run ascend-descend algorithms (such as bitonic sort) on the faulty hypercube by implementing them on the embedded CCC. We then consider hypercubes with both edge and node faults. We prove that for any constant c there exists a fault-free subgraph of an n-dimensional hypercube with nc faulty components that can implement a large class of hypercube algorithms with only a constant factor slowdown. To the best of our knowledge, this result is the first in which a hypercube can tolerate more than O(n) faults in the worst case sense.