Processor allocation in an N-cube multiprocessor using gray codes
IEEE Transactions on Computers
Information and Computation
Hyperswitch network for the hypercube computer
ISCA '88 Proceedings of the 15th Annual International Symposium on Computer architecture
Performance of the Direct Binary n-Cube Network for Multiprocessors
IEEE Transactions on Computers
Fast computation using faulty hypercubes
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Subcube Allocation in Hypercube Computers
IEEE Transactions on Computers
A Fast Recognition-Complete Processor Allocation Strategy for Hypercube Computers
IEEE Transactions on Computers
Tolerating Faults in Hypercubes Using Subcube Partitioning
IEEE Transactions on Computers - Special issue on fault-tolerant computing
A Top-Down Processor Allocation Scheme for Hypercube Computers
IEEE Transactions on Parallel and Distributed Systems
A New Graph Approach to Minimizing Processor Fragmentation in Hypercube Multiprocessors
IEEE Transactions on Parallel and Distributed Systems
Optimal Subcube Fault Tolerance in a Circuit-Switched Hypercube
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
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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驴 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驴 1)-cube in a faulty n-cube. In general, we show that a fault-free (n驴m驴 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.