The connection machine
Information and Computation
Topological Properties of Hypercubes
IEEE Transactions on Computers
Reliable Broadcast in Hypercube Multicomputers
IEEE Transactions on Computers
The iPSC/2 direct-connect communications technology
C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1
Fast computation using faulty hypercubes
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Designing fault-tolerant systems using automorphisms
Journal of Parallel and Distributed Computing
Coding theory, hypercube embeddings, and fault tolerance
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Tolerating Faults in Hypercubes Using Subcube Partitioning
IEEE Transactions on Computers - Special issue on fault-tolerant computing
A Fault-Tolerant Communication Scheme for Hypercube Computers
IEEE Transactions on Computers
Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions
IEEE Transactions on Computers
Depth-First Search Approach for Fault-Tolerant Routing in Hypercube Multicomputers
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Algorithms and Bounds for Shortest Paths and Diameter in Faulty Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Embedding and Reconfiguration of Binary Trees in Faulty Hypercubes
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
Unicast in Hypercubes with Large Number of Faulty Nodes
IEEE Transactions on Parallel and Distributed Systems
SAC '97 Proceedings of the 1997 ACM symposium on Applied computing
Fault-Tolerant Routing in Hypercube Multicomputers Using Local Safety Information
IEEE Transactions on Parallel and Distributed Systems
Improved One-to-All Broadcasting Algorithms on Faulty SIMD Hypercubes
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Spare processor allocation for fault tolerance in torus-based multicomputers
FTCS '96 Proceedings of the The Twenty-Sixth Annual International Symposium on Fault-Tolerant Computing (FTCS '96)
Research note: Improved one-to-all broadcasting algorithms on faulty SIMD hypercubes
Journal of Parallel and Distributed Computing
WOC '08 Proceedings of the Eighth IASTED International Conference on Wireless and Optical Communications
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Hypercube network is an attractive structure for parallel processing due to its symmetry and regularity. In this paper, we use the concept of free dimensions to achieve fault tolerance in hypercubes without requiring additional spare processing nodes; such additional redundancy requires modification of hypercube structure. A free dimension is defined to be a dimension across which both end nodes are not faulty.Given an n-dimensional hypercube, Qn, and a set of f驴n faulty nodes, we present an efficient algorithm to find free dimensions, and show that at least n驴f+ 1 free dimensions exist. Free dimensions can be used to partition Qn into subcubes such that each subcube contains at most one fault. Such a partitioning helps in achieving fault tolerance via emulation, embedding, reconfiguration. It also helps in designing efficient routing and broadcasting algorithms in faulty hypercubes.