IEEE Transactions on Computers
Topological Properties of Hypercubes
IEEE Transactions on Computers
A simple parallel tree contraction algorithm
Journal of Algorithms
Concrete Math
Fibonacci Cubes-A New Interconnection Topology
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)
On the Sizes of Extended Fibonacci Cubes
IEEE Transactions on Parallel and Distributed Systems
The Postal Network: A Recursive Network for Parameterized Communication Model
The Journal of Supercomputing
Embedding Fibonacci Cubes into Hypercubes with Omega(2cn) Faulty Nodes
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Observability of the extended Fibonacci cubes
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Minimal change list for Lucas strings and some graph theoretic consequences
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
Cube Polynomial of Fibonacci and Lucas Cubes
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
A fault-tolerant routing strategy for fibonacci-class cubes
ACSAC'05 Proceedings of the 10th Asia-Pacific conference on Advances in Computer Systems Architecture
Note: Fibonacci (p, r)-cubes which are median graphs
Discrete Applied Mathematics
Hi-index | 0.00 |
The Fibonacci Cube is an interconnection network that possesses many desirable properties that are important in network design and application. The Fibonacci Cube can efficiently emulate many hypercube algorithms and uses fewer links than the comparable hypercube, while its size does not increase as fast as the hypercube. However, most Fibonacci Cubes (more than 2/3 of all) are not Hamiltonian. In this paper, we propose an Extended Fibonacci Cube (EFC1) with an even number of nodes. It is defined based on the same sequence F(i) = F(i驴 1) + F(i驴 2) as the regular Fibonacci sequence; however, its initial conditions are different. We show that the Extended Fibonacci Cube includes the Fibonacci Cube as a subgraph and maintains its sparsity property. In addition, it is Hamiltonian and is better in emulating other topologies. Specifically, the Extended Fibonacci Cube can embed binary trees more efficiently than the regular Fibonacci Cube and is almost as efficient as the hypercube, even though the Extended Fibonacci Cube is a much sparser network than the hypercube. We also propose a series of Extended Fibonacci Cubes with even number of nodes. Any Extended Fibonacci Cube (EFCk, with k驴 1) in the series contains the node set of any other cube that precedes EFCk in the series. We show that any Extended Fibonacci Cube maintains virtually all the desirable properties of the Fibonacci Cube. The EFCks can be considered as flexible versions of incomplete hypercubes, which eliminates their restriction on the number of nodes, and, thus, makes it possible to construct parallel machines with arbitrary sizes.