A Bandwidth-Optimal All-to-All Communication in Two-Dimensional Fully Connected Network

High-radix direct interconnection networks enable many simultaneous, non-blocking point-to-point communications at every compute node of high-performance computing systems. This feature provides a novel opportunity to improve the performance of collective communications. In this study, we focus on two-dimensional fully connected network topologies (2dfc) which are basic blocks of cutting-edge high-radix network topologies such as Dragonfly and HyperX. We aim to design a bandwidth-optimal algorithm for the All-to-All collective communication in the 2dfc network. By using parallel point-to-point communications, the proposed algorithm enables parallel non-blocking intra- and inter-group communications with striping data placement. Simulation results using SimGrid illustrated that the proposed algorithm outperforms the conventional algorithms significantly. Compared with topology-aware algorithms, the proposed approach reduces 1.66× and 1.58× communication time of an existing and a topology-aware collective algorithm in a 16 × 16 2dfc network, respectively.