A Fault-Free Unicast Algorithm in the Generalized Hypercube with Restricted Faulty Vertices.

The generalized hypercube is a highly-connective network proposed by Bhuyan and Agrawal. In this paper, we study the restricted connectivity and fault-free unicast algorithm in the generalized hypercube. Firstly, we prove that the restricted connectivity of a r -dimensional generalized hypercube G (m r , m r − 1 , … , m 1) is 2 κ (G) − n , where κ (G) denotes the connectivity of G (m r , m r − 1 , … , m 1) and n = max { m 1 , m 2 , … , m r } , under the condition that each vertex has at least one fault-free neighbor. It is almost twice the traditional connectivity of G (m r , m r − 1 , … , m 1). Furthermore, we present an O (κ (G) 3) fault-free unicast algorithm in the generalized hypercube. [ABSTRACT FROM AUTHOR]