Star-product graphs are a natural extension of the Cartesian product, but have not been well-studied. We show that many important established and emerging network topologies, including HyperX, SlimFly, BundleFly, PolarStar, mesh, and torus, are in fact star-product graphs. While this connection was known for BundleFly and PolarStar, it was not for the others listed. We extend a method of constructing maximal and near-maximal sets of edge-disjoint spanning trees on Cartesian products to the star product, thus obtain maximal or near-maximal sets of edge-disjoint spanning trees on new networks of importance, where such sets can improve bandwidth of collective operations and therefore accelerate many important workloads in high-performance computing.

翻译：星积图是笛卡尔积的一种自然推广，但尚未得到充分研究。我们证明了包括HyperX、SlimFly、BundleFly、PolarStar、网格以及环面在内的许多重要已建立和新兴网络拓扑结构实际上都是星积图。虽然BundleFly和PolarStar与星积图的关联已知，但其他拓扑结构此前未被揭示。我们将笛卡尔积上构造最大或近最大边不交生成树集合的方法推广至星积图，从而在具有重要价值的新兴网络中获得了最大或近最大边不交生成树集合——这类集合可提升集合通信操作的带宽，进而加速高性能计算中的许多关键工作负载。