Processor allocation in an N-cube multiprocessor using gray codes
IEEE Transactions on Computers
Topological Properties of Hypercubes
IEEE Transactions on Computers
Distributed fault-tolerant embeddings of rings in hypercubes
Journal of Parallel and Distributed Computing
Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions
IEEE Transactions on Computers
Combinatorial Algorithms: Theory and Practice
Combinatorial Algorithms: Theory and Practice
An Intuitive and Effective New Representation for Interconnection Network Structures
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
ICPADS '06 Proceedings of the 12th International Conference on Parallel and Distributed Systems - Volume 1
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube
Journal of Combinatorial Optimization
Hi-index | 14.98 |
To embed a ring in a hypercube is to find a Hamiltonian cycle through every node of the hypercube. It is obvious that no 2n-node Hamiltonian cycle exists in an n-dimensional faulty hypercube which has at least one faulty node. However, if a hypercube has faulty links only and the number of faulty links is at most n-2, at least one 2n-node Hamiltonian cycle can be found. In this paper, we propose a distributed ring-embedding algorithm that can find a Hamiltonian cycle in a fault-free or faulty n-dimensional hypercube (Q,), and the complexity is O(n) parallel steps. The algorithm is based on the recursion property of the hypercube and the free-link dimension concept. In some cases, even when the number of faulty links is larger than n-2, Hamiltonian cycles may still exist. We show that the largest possible number of faulty links that can be tolerated is 2n-1-1. The performance and the constraints of the fault-tolerant algorithm is also analyzed in detail in this paper. Furthermore, a dynamic reconfiguration algorithm for an embedded ring is proposed and discussed. Due to the distributed nature of the algorithms, they are useful for the simulation of ring-based multiprocessors on MIMD hypercube multiprocessors