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Tolerating Faults in Hypercubes Using Subcube Partitioning
May 1992 (vol. 41 no. 5)
pp. 599-605

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.

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Index Terms:
fault tolerance; node faults; subcube partitioning; edge faults; worst-case distribution; faulty components; fault-tree subgraph; hypercube algorithms; computational complexity; fault tolerant computing; graph theory; hypercube networks; parallel algorithms.
Citation:
J. Bruck, R. Cypher, D. Soroker, "Tolerating Faults in Hypercubes Using Subcube Partitioning," IEEE Transactions on Computers, vol. 41, no. 5, pp. 599-605, May 1992, doi:10.1109/12.142686
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