# A Recursive Algorithm for Constructing Dual-CISTs in Hierarchical Folded Cubic Networks

Hsin-Jung Lin, Shyue-Ming Tang, Kung-Jui Pai, Jou-Ming Chang- Computer Science (miscellaneous)

Let [Formula: see text] be a set of [Formula: see text] spanning trees in a graph [Formula: see text]. The [Formula: see text] spanning trees are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices [Formula: see text] and [Formula: see text] in any two trees have neither vertex nor edge in common except for [Formula: see text] and [Formula: see text]. Particularly, [Formula: see text] is called a dual-CIST provided [Formula: see text]. For data transmission applications in reliable networks, the existence of a dual-CIST can provide a configuration of fault-tolerant routing called protection routing. This paper investigates the problem of constructing a dual-CIST in the [Formula: see text]-dimensional hierarchical folded cubic network [Formula: see text]. The network is a two-level network using folded hypercube [Formula: see text] as clusters to reduce the diameter, hardware overhead and improve the fault tolerance ability. We propose a recursive algorithm to construct a dual-CIST of [Formula: see text] in [Formula: see text] time for [Formula: see text], where the time required is the same scale as the number of vertices of [Formula: see text]. Also, the diameter of each constructed CIST is [Formula: see text].