An improved algorithm to construct edge-independent spanning trees in augmented cubes

Abstract

Edge-Independent spanning trees (EISTs) can be used in IP fast rerouting to guarantee recovery from link failures, as well as in data broadcasting in networks to enhance fault-tolerance, bandwidth, and security. The n-dimensional augmented cube AQn is an important node-symmetric variant of the n-dimensional hypercube Qn. Recently, Wang et al. proposed a method to construct 2n−1 EISTs in AQn (Wang et al., 2017). However, the height of the tallest EIST is no less than n+2. Since height is an important performance indicator of the EISTs, in this paper, we further study the existence and construction of EISTs in augmented cubes with lower heights. We first propose a constructive algorithm to construct 2n−1 trees rooted at any node in AQn. We then prove the 2n−1 trees obtained by the algorithm are 2n−1 EISTs with the maximal height n, and the time complexity of the algorithm is O(NlogN), where N=2n is the number of nodes in AQn.