A Simple Parallel Algorithm for Constructing Independent Spanning Trees on Twisted Cubes∗

In 1989, Zehavi and Itai [46] proposed the following conjecture: a k-connected graph G must possess k independent spanning trees (ISTs for short) with an arbitrary node as the common root. An n-dimensional twisted cube, denoted by TQn, is a variation of hypercubes with connectivity n to achieving some improvements of structure properties. Recently, Yang [42] proposed an algorithm for constructing n edge-disjoint spanning trees in TQn for any odd integer n > 3. Moreover, he showed that half of them are ISTs. At a later stage, Wang et al. [32] confirm the ISTs conjecture by providing an O(N logN) algorithm to construct n ISTs rooted at an arbitrary node on TQn, where N = 2 n is the number of nodes in TQn. However, this algorithm is executed in a recursive fashion and thus are hard to be parallelized. In this paper, we present a non-recursive and fully parallelized approach to construct n ISTs rooted at an arbitrary node of TQn in O(logN) time using N processors. In particular, the constructing rule of spanning trees is simple and the proof of independency is easier than ever before. Keyword: independent spanning trees; interconnection networks; twisted cubes;