On the maximal connected component of hypercube with faulty vertices

Abstract

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n-dimensional cube with faulty processors. We first prove that an n-cube with a set F of at most 2n − 3 failing processors has a component of size ≥2 ⁿ  − |F| − 1. We then prove that an n-cube with a set F of at most 3n − 6 missing processors has a component of size ≥2 ⁿ  − |F| − 2.

Keywords:

• Interconnection network
• Fault tolerance
• Maximal connected component
• Hypercube

Acknowledgements

This research was partly supported by the Visiting Scholar's Funds of National Education Ministry's Key Laboratory of Electro-Optical Technique and System, Chongqing University.