Towards the Independent Spanning Trees in Conditional BC Networks

Abstract

-Independent spanning trees (ISTs for short) in networks have applications such as reliable communication protocols, the multi-node broadcasting, one-to-all broadcasting, reliable broadcasting, and secure message distribution. However, it is an open problem whether there are n ISTs rooted at any node in any n  connected network with 5 n  . In this paper, we consider the construction of ISTs in a family of hypercube variants, called conditional BC networks. A recursive algorithm based on two common rules is proposed to construct n ISTs rooted at any node in any n -dimensional conditional BC network n X . We also show that our constructive method is adaptive to not only the existing hypercube variants, but also some other ones.Index Terms -Conditional BC network, independent spanning trees, node-disjoint paths, recursive algorithm.