Issue No. 05 - May (1992 vol. 41)

ISSN: 0018-9340

pp: 599-605

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.142686

ABSTRACT

<p>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.</p>

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

R. Cypher, D. Soroker, J. Bruck, "Tolerating Faults in Hypercubes Using Subcube Partitioning",

*IEEE Transactions on Computers*, vol. 41, no. , pp. 599-605, May 1992, doi:10.1109/12.142686