Simulation of Complete Binary Tree Structures in a Faulty Flexible Hypercube

Abstract

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.