Construction independent spanning trees on locally twisted cubes in parallel

Let $$LTQ_n$$ L T Q n be the n-dimensional locally twisted cube. Hsieh and Tu (Theor Comput Sci 410(8–10):926–932, 2009) proposed an algorithm to construct n edge-disjoint spanning trees rooted at a particular vertex 0 in $$LTQ_n$$ L T Q n . Later on, Lin et al. (Inf Process Lett 110(10):414–419, 2010) 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 $$v(\ne r)$$ v ( ≠ r ) , the paths from v to r in any two trees are internally vertex-disjoint. Shortly afterwards, Liu et al. (Theor Comput Sci 412(22):2237–2252, 2011) pointed out that $$LTQ_n$$ L T Q n fails to be vertex-transitive for $$n\geqslant 4$$ n ⩾ 4 and proposed an algorithm for constructing n ISTs rooted at an arbitrary vertex in $$LTQ_n$$ L T Q n . Although this algorithm can simultaneously construct n ISTs, it is hard to be parallelized for the construction of each spanning tree. In this paper, from a modification of Hsieh and Tu’s algorithm, we present a fully parallelized scheme to construct n ISTs rooted at an arbitrary vertex in $$LTQ_n$$ L T Q n in $${\mathcal O}(n)$$ O ( n ) time using $$2^n$$ 2 n vertices of $$LTQ_n$$ L T Q n as processors.