Embedded Edge-Connectivity Reliability Evaluation of Augmented Hypercube Interconnection Networks

Abstract

In the contemporary world, to meet the increasing need to deal with massive data, the interconnection networks for large-scale parallel and distributed systems need to expand for stronger scalability requirements. Let [Formula: see text] be a recursive [Formula: see text]-dimensional network. Since the presence of faulty links or processors may disconnect the entire network, one hopes that every remaining processor lies in an undamaged lower-dimensional subnetwork. Under this circumstance, in 2012, Yang and Wang first proposed the conception of [Formula: see text]-embedded edge-connectivity [Formula: see text] of [Formula: see text], which is defined as the minimum number of links whose removal results in several disconnected components, and each processor is contained in an [Formula: see text]-dimensional subnetwork [Formula: see text]. The augmented cube, denoted by [Formula: see text], proposed by Choudum and Sunitha, is a momentous variant of the hypercube as an interconnection topology of parallel computing. It retains many favorable properties of the hypercube and possesses several embedded properties that the hypercube and other variations do not have. For [Formula: see text] and [Formula: see text], this paper determines [Formula: see text]-embedded edge-connectivity of [Formula: see text]-dimensional augmented cube, [Formula: see text], and shows exact values [Formula: see text], where [Formula: see text] if [Formula: see text], and [Formula: see text] otherwise. The parameters can provide more accurate measurements for the reliability and fault-tolerance of the corresponding systems.