A parallel algorithm for constructing multiple independent spanning trees in bubble-sort networks

The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number advantages, including the increase fault-tolerance and secure message distribution. Thus, designs ISTs on several classes have been widely investigated. Kao et al. [Journal Combinatorial Optimization 38 (2019) 972-986] proposed an algorithm to construct bubble-sort networks. is executed recursive function thus hard parallelize. In this paper, we focus problem constructing Bn present non-recursive algorithm. Our approach can be fully parallelized, i.e., every vertex determine its parent each tree constant time. This solves open from paper by Furthermore, show that total time complexity O(n⋅n!) our asymptotically optimal, where n dimension n! vertices network.