Edge-independent spanning trees in folded crossed cubes

Abstract

Edge-independent spanning trees (for short EISTs) have widespread applications in fault-tolerance to enhance stability and security of networks, as well as in IP fast rerouting to prevent network breakdown caused by link failure. Then, the algorithms for constructing EISTs on many classes of graphs have been investigated. The folded crossed cube was proposed based on the folded cube and the crossed cube, which possesses such appealing properties as short diameter, short mean internode distance and very low message traffic density. In this paper, we study the existence and construction of EISTs with the same root r in the n-dimensional folded crossed cube (for short FCQn). For v∈V(FCQn)∖{r} and i∈{0,1,⋯,n−1}, we first propose two algorithms to obtain the sequence Sv,i and the set Fv, respectively. Then, based on them, an algorithm with time complexity O(n2) by using N processors is proposed to construct n+1 EISTs rooted at any vertex r in FCQn, where N=2n. And the corresponding theoretical proof and simulation experiments are presented to verify its validity. Since FCQn is (n+1)-regular, the result is optimal with respect to the number of EISTs constructed. Moreover, the performance of the proposed algorithm is evaluated experimentally in terms of average distance and average distance-diameter ratio of resulting EISTs.