Construction of optimal independent spanning trees on folded hypercubes

• Authors: Xie-Bin Chen
• Venue: Information Sciences: an International Journal
• Year: 2013

The n-dimensional folded hypercube FQ"n is an important variant of the n-dimensional hypercube Q"n, which is obtained from Q"n by adding an edge between any pair of vertices with complementary addresses. The diameter of FQ"n is @?n/2@?, about half the diameter of Q"n. A set of k(=2) spanning trees rooted at the same vertex r in a graph G is said to be independent if for each vertex x other than r, the k paths from r to x, with one path in each spanning tree, are internally disjoint. By using independent spanning trees (ISTs) one can design fault-tolerant broadcasting schemes and increase message security in a network. Recently, Yang et al. proposed an algorithm, which can be parallelized, for constructing n+1 ISTs on FQ"n with the height of each spanning tree being n. In this paper, we propose an algorithm for constructing n+1 optimal ISTs on FQ"n in the sense that there is a shortest path between the only child of the root r and any other vertex in each spanning tree (therefore, the height of each spanning tree is @?n/2@?+1). Moreover, the algorithm runs in time O((n+1)N) and can be parallelized to run by using N=2^n processors on FQ"n in time O(n).