The Wide Diameter and Fault Diameter of Exchanged Crossed Cube

The fault diameter and wide diameter are commonly used to measure the fault tolerance and transmission delay of interconnection networks beyond traditional diameter. The alpha-wide diameter of graph G, denoted by D-alpha(G), is the minimum integer l such that there exist at least alpha internally vertex disjoint paths of length at most l for any two distinct vertices in G. The beta-fault diameter of graph G, denoted by D-beta(f)(G), is the maximum diameter of the survival graph obtained by deleting at most beta vertices in G. The exchanged crossed cube, as a compounded interconnection network denoted by ECQ(s; t), holds the desirable properties of both crossed cube and exchanged hypercube, while achieving a better balanced between cost and performance of the parallel computing systems. In this paper, we construct s + 1 internally vertex disjoint paths between any two distinct vertices of ECQ(s; t). Moreover, we determine the upper and lower bounds of (s + 1)-wide diameter and s-fault diameter of ECQ(s; t), i.e., inverted right perpendicular s/2 inverted left perpendicular + inverted right perpendicular t+1/2 inverted left perpendicular + 4 <= D-s(f) (ECQ(s; t)) <= Ds+1(ECQ(s; t)) <= inverted right perpendicular s+1/2 inverted left perpendicular + inverted right perpendicular t+1/2 inverted left perpendiculare + 5, whichshows that the exchanged crossed cube has better efficiency and reliability than that of the exchanged hypercube.

Automated summary

This paper investigates the wide diameter and fault diameter of the exchanged crossed cube (ECQ), and evaluates its performance and reliability by constructing internally vertex disjoint paths. The upper and lower bounds of these diameters are determined, demonstrating that ECQ is more efficient and reliable than the exchanged hypercube.