Construction independent spanning trees on locally twisted cubes in parallel

Let LTQn denote the n-dimensional locally twisted cube. Hsieh and Tu (2009) [13] presented an algorithm to construct n edge-disjoint spanning trees rooted at vertex 0 in LTQn. Later on, Lin et al. (2010) [23] proved that Hsieh and Tu’s spanning trees are indeed independent spanning trees (ISTs for short), i.e., all spanning trees are rooted at the same vertex r and for any other vertex v(6= r), the paths from v to r in any two trees are vertex-disjoint except the two end vertices v and r. Shortly afterwards, Liu et al. (2011) [24] pointed out that LTQn fails to be vertex-transitive for n > 4 and proposed an algorithm for constructing n ISTs rooted at an arbitrary vertex of LTQn. Although this algorithm can simultaneously construct n ISTs in parallel, it is not fully parallelized for the construction of each spanning tree. In this paper, we revisit the problem of constructing n ISTs rooted at an arbitrary vertex of LTQn. As a consequence, we present a fully parallelized approach that is obtained from Hsieh and Tu’s algorithm with a slight modification. Keyword: independent spanning trees; edgedisjoint spanning trees; locally twisted cubes; interconnection networks; fault-tolerant broadcasting;