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Subcube Fault Tolerance in Hypercube Multiprocessors
September 1995 (vol. 44 no. 9)
pp. 1108-1120

Abstract—In this paper, we study the problem of constructing subcubes in faulty hypercubes. First a divide-and-conquer technique is used to form the set of disjoint subcubes in the faulty hypercube. The concept of irregular subcubes is then introduced to take advantage of advanced switching techniques, such as wormhole routing, to increase the sizes of the available subcubes. We present a subcube partitioning technique to form an irregular subcube of maximum size. The n-cube containing two faults is studied first because, in the worst case, two faults are sufficient to destroy all the possible regular (n− 1)-cubes. It is shown that the subcube partitioning technique is able to tolerate $\lceil {n \over 2}\rceil$ faults while maintaining a fault-free (n− 1)-cube in a faulty n-cube. In general, we show that a fault-free (nm− 1)-cube is guaranteed when there are $( \lceil {n -m \over 2}\rceil + 1) \times 2^m + 2^{m-1} -1$ or fewer faults. We also develop a two-phase subcube allocation strategy in order to show the average case performance of our subcube construction technique. Extensive simulation is conducted to show the effectiveness of the two-phase subcube allocation strategy.

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Index Terms:
Hypercube, subcube partitioning, fault tolerance, wormhole routing.
Laxmi N. Bhuyan, Yeimkuan Chang, "Subcube Fault Tolerance in Hypercube Multiprocessors," IEEE Transactions on Computers, vol. 44, no. 9, pp. 1108-1120, Sept. 1995, doi:10.1109/12.464389
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