Reconfiguring a hypercube in the presence of faults
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Fast computation using faulty hypercubes
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Distributed fault-tolerant embeddings of rings in hypercubes
Journal of Parallel and Distributed Computing
Optimal Specified Root Embedding of Full Binary Trees in Faulty Hypercubes
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Structural and Tree Embedding Aspects of Incomplete Hypercubes
IEEE Transactions on Computers
Optimal Simulation of Full Binary Trees on Faulty Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes
IEEE Transactions on Parallel and Distributed Systems
Embedding and Reconfiguration of Spanning Trees in Faulty Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs
IEEE Transactions on Parallel and Distributed Systems
Embedding Cube-Connected Cycles Graphs into Faulty Hypercubes
IEEE Transactions on Computers
Free Dimensions-An Effective Approach to Achieving Fault Tolerance in Hypercubes
IEEE Transactions on Computers
Embedding Fibonacci Cubes into Hypercubes with Omega(2cn) Faulty Nodes
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Optimal Path Embedding in Crossed Cubes
IEEE Transactions on Parallel and Distributed Systems
Fault-Free pairwise independent hamiltonian paths on faulty hypercubes
ACSAC'06 Proceedings of the 11th Asia-Pacific conference on Advances in Computer Systems Architecture
Embedding of cycles in the faulty hypercube
ACSAC'05 Proceedings of the 10th Asia-Pacific conference on Advances in Computer Systems Architecture
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The focus is on the following graph-theoretic question associated with the simulation ofcomplete binary trees by faulty hypercubes: if a certain number of nodes or links areremoved from an n-cube, will an (n-1)-tree still exists as a subgraph? While the generalproblem of determining whether a k-tree, kn, still exists when an arbitrary number ofnodes/links are removed from the n-cube is found to be NP-complete, an upper bound isfound on how many nodes/links can be removed and an (n-1)-tree still be guaranteed toexist. In fact, as a corollary of this, it is found that if no more than n-3 nodes/links areremoved from an (n-1)-subcube of the n-cube, an (n-1)-tree is also guaranteed to exist.