Flexible Hypercube Research Articles

Fault-tolerant mapping of a mesh network in a flexible hypercube

The Flexible Hypercube FHN is an important variant of the Hypercube Hn and possesses many desirable properties for interconnection networks. This paper proposes a novel algorithm of fault-tolerant ...

Embedding of complete binary tree with 2-expansion in a faulty Flexible Hypercube

Abstract Although the embedding of complete binary trees in faulty hypercubes has received considerable attention, to our knowledge, no paper has demonstrated how to embed a complete binary tree in a faulty Flexible Hypercube. Therefore, this investigation presents an algorithm to facilitate the embedding job when the Flexible Hypercube contains faulty nodes. Of particular concern are the network structures of the Flexible Hypercube that balance the load before as well as after faults start to degrade the performance of the Flexible Hypercube. Furthermore, to obtain the replaceable node of the faulty node, 2-expansion is permitted such that up to (n−2) faults can be tolerated with congestion 1, dilation 4 and load 1.

On fault-tolerant embedding of Hamiltonian cycles, linear arrays and rings in a Flexible Hypercube

The Hamiltonian cycle of a Flexible Hypercube graph network is investigated in this paper. The result can readily be used in the optimal embedding of a linear array (or a ring) of processors in a faulty Flexible Hypercube. There are embedding algorithms proposed in this paper. These embedding algorithms show a ring with any number of nodes that can be embedded into a faulty Flexible Hypercube with load 1, congestion 1 and dilation 3 such that O( n 2−(⌊log 2 m⌋) 2) faults can be tolerated, where n is the dimension of the Flexible Hypercube and m is the number of nodes of the ring.

Simulation of Complete Binary Tree Structures in a Faulty Flexible Hypercube

The Flexible Hypercube is a generalization of binary hypercube networks in that the number of nodes can be arbitrary in contrast to a strict power of 2. Restated, the Flexible Hypercube retains the connectivity and diameter properties of the corresponding hypercube. Although the embedding of complete binary trees in faulty hypercubes has received considerable attention, to our knowledge, no paper has demonstrated how to embed a complete binary tree in a faulty Flexible Hypercube. Therefore, this investigation presents a novel algorithm to facilitate the embedding job when the Flexible Hypercube contains faulty nodes. Of particular concern are the network structures of the Flexible Hypercube that balance the load before as well as after faults start to degrade the performance of the Flexible Hypercube. Furthermore, to obtain the replaceable node of the faulty node, 2-expansion is permitted such that up to (n − 2) faults can be tolerated with congestion 1, dilation 4 and load 1. That is, (n − 1) is the dimension of a Flexible Hypercube. Results presented herein demonstrate that embedding methods are optimized.

The Flexible Hypercube: A New Fault-Tolerant Architecture for Parallel Computing

This paper presents the new Flexible Hypercube architecture. The Flexible Hypercube is a fault-tolerant network topology that can be constructed for an arbitrary number of nodes and is incrementally expandable. This topology maintains the strong features of the Hypercube while overcoming deficiencies in expandability. It is shown to have strong node connectivity, a small diameter, and to be tolerant of faults. The Flexible Hypercube is a suitable architecture for the design of both tightly coupled parallel systems and distributed systems. Efficient fault-free and fault-tolerant algorithms for message routing and broadcasting are presented for the architecture. The fault-free algorithm guarantees successful routing inO(logN) time, whereNis the number of nodes in the system, and the fault-tolerant algorithm guarantees routing to functioning nodes if a route exists. The fault-free and fault-tolerant broadcasting algorithms have time complexityO(logN), and the fault-tolerant algorithm guarantees success if no two faulty nodes are adjacent and no functioning node is adjacent to two faults.