Reconfiguring a hypercube in the presence of faults
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Embedding and Reconfiguration of Binary Trees in 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
Fibonacci Cubes-A New Interconnection Topology
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
Near-Optimal Embeddings of Trees into Fibonacci Cubes
SSST '96 Proceedings of the 28th Southeastern Symposium on System Theory (SSST '96)
ICPP '93 Proceedings of the 1993 International Conference on Parallel Processing - Volume 01
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Fibonacci Cubes are special subgraphs of hypercubes based on Fibonacci numbers. We present a construction of a direct embedding of a Fibonacci Cube of dimension n into a faulty hypercube of dimension n with less or equal 2⌈n/4⌉-1 faults. In fact, there exists a direct embedding of a Fibonacci Cube of dimension n into a faulty hypercube of dimension n with at most 2n/4fn faults (fn is the n-th Fibonacci number). Thus the number Φ(n) of tolerable faults grows exponentially with respect to dimension n, Φ(n) = Ω(2cn), for c = 2-log2(1+√5) = 0:31. On the other hand, Φ(n) = O(2dn), for d = (8-3 log2 3)/4 = 0.82. As a corollary, there exists a nearly polynomial algorithm constructing a direct embedding of a Fibonacci Cube of dimension n into a faulty hypercube of dimension n (if it exists) provided that faults are given on input by enumeration. However, the problem is NP-complete, if faults are given on input with an asterisk convention.